What is the HCF of (18) and (24) using prime factorisation?
Correct answer: B
Step 1: (18=2\times3^2) and (24=2^3\times3). Step 2: Taking the smaller powers of common prime factors gives (2\times3=6). Step 3: For HCF, take only common prime factors.
Mathematics
HCF and LCM using prime factorisation
अभाज्य गुणनखंडन द्वारा महत्तम समापवर्तक और लघुत्तम समापवर्त्य
In this Class 10 Mathematics topic from Real Numbers, students learn to find the HCF and LCM of two or more numbers through prime factorisation. They break each number into prime factors, compare the resulting powers, and select the appropriate common factors: the lowest powers for HCF and the highest powers for LCM. The topic also develops accuracy in writing factor trees, simplifies comparison between methods, and helps students apply these concepts to numerical and everyday problem-solving situations.
TOPIC PRACTICE
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Up to 25 questions from this page. Select your focus, then start.
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Easy · Level 1
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- (3)
- (6)
- (9)
- (12)
Easy · Level 1
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- (36)
- (48)
- (72)
- (144)
Easy · Level 1
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- (10)
- (20)
- (30)
- (40)
Easy · Level 1
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- (60)
- (100)
- (120)
- (240)
Easy · Level 1
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- (5)
- (10)
- (15)
- (25)
Easy · Level 1
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- (150)
- (225)
- (300)
- (375)
Easy · Level 1
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- (8)
- (12)
- (16)
- (24)
Easy · Level 1
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- (48)
- (96)
- (128)
- (192)
Easy · Level 1
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- (3)
- (6)
- (9)
- (12)
Easy · Level 1
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- (54)
- (72)
- (108)
- (216)
Easy · Level 1
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- (6)
- (9)
- (18)
- (36)
Easy · Level 1
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- (180)
- (240)
- (360)
- (720)
Easy · Level 1
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- (2)
- (3)
- (6)
- (12)
Easy · Level 1
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- (60)
- (90)
- (120)
- (180)
Easy · Level 1
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- (4)
- (8)
- (12)
- (16)
Easy · Level 1
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- (120)
- (160)
- (240)
- (480)
Easy · Level 1
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- (15)
- (30)
- (45)
- (90)
Easy · Level 1
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- (90)
- (120)
- (180)
- (240)
Easy · Level 1
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- (12)
- (18)
- (24)
- (36)
Easy · Level 1
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- (24)
- (36)
- (48)
- (72)
Easy · Level 1
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- (20)
- (171)
- (1620)
- (1890)
Easy · Level 1
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- (156)
- (1728)
- (1440)
- (1200)
Easy · Level 1
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- (60)
- (144)
- (432)
- (864)
Easy · Level 1
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- (48)
- (60)
- (72)
- (120)
Easy · Level 1
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- (3)
- (6)
- (9)
- (12)
What is the LCM of (18) and (24) using prime factorisation?
Correct answer: C
Step 1: (18=2\times3^2) and (24=2^3\times3). Step 2: Taking the highest powers of all prime factors gives (2^3\times3^2=72). Step 3: For LCM, include both common and uncommon prime factors.
What is the HCF of (40) and (60)?
Correct answer: B
Step 1: (40=2^3\times5) and (60=2^2\times3\times5). Step 2: The common factors with smaller powers are (2^2) and (5). Step 3: (2^2\times5=20), so the HCF is (20).
What is the LCM of (40) and (60)?
Correct answer: C
Step 1: (40=2^3\times5) and (60=2^2\times3\times5). Step 2: Use the highest powers (2^3), (3), and (5). Step 3: (2^3\times3\times5=120), so the LCM is (120).
What will be the HCF of (45) and (75)?
Correct answer: C
Step 1: (45=3^2\times5) and (75=3\times5^2). Step 2: Take the smaller powers of the common prime factors (3) and (5). Step 3: (3\times5=15), so the HCF is (15).
What will be the LCM of (45) and (75)?
Correct answer: B
Step 1: (45=3^2\times5) and (75=3\times5^2). Step 2: Take the highest powers (3^2) and (5^2). Step 3: (3^2\times5^2=225), so the LCM is (225).
Which is the HCF of (32) and (48)?
Correct answer: C
Step 1: (32=2^5) and (48=2^4\times3). Step 2: The only common prime factor is (2), and the smaller power is (2^4). Step 3: (2^4=16), so the HCF is (16).
Which is the LCM of (32) and (48)?
Correct answer: B
Step 1: (32=2^5) and (48=2^4\times3). Step 2: Take the highest powers (2^5) and (3). Step 3: (2^5\times3=96), so the LCM is (96).
What is the HCF of (27) and (36)?
Correct answer: C
Step 1: (27=3^3) and (36=2^2\times3^2). Step 2: The common prime factor is (3), and the smaller power is (3^2). Step 3: (3^2=9), so the HCF is (9).
What is the LCM of (27) and (36)?
Correct answer: C
Step 1: (27=3^3) and (36=2^2\times3^2). Step 2: For LCM, take the highest powers (2^2) and (3^3). Step 3: (2^2\times3^3=108), so the LCM is (108).
What is the HCF of (72) and (90)?
Correct answer: C
Step 1: (72=2^3\times3^2) and (90=2\times3^2\times5). Step 2: The smaller powers of common factors are (2) and (3^2). Step 3: (2\times9=18), so the HCF is (18).
What is the LCM of (72) and (90)?
Correct answer: C
Step 1: (72=2^3\times3^2) and (90=2\times3^2\times5). Step 2: The highest powers are (2^3), (3^2), and (5). Step 3: (8\times9\times5=360), so the LCM is (360).
What is the HCF of (12), (18), and (30)?
Correct answer: C
Step 1: (12=2^2\times3), (18=2\times3^2), and (30=2\times3\times5). Step 2: The common prime factors in all three numbers are (2) and (3). Step 3: (2\times3=6), so the HCF is (6).
What is the LCM of (12), (18), and (30)?
Correct answer: D
Step 1: (12=2^2\times3), (18=2\times3^2), and (30=2\times3\times5). Step 2: Use the highest powers (2^2), (3^2), and (5). Step 3: (4\times9\times5=180), so the LCM is (180).
What will be the HCF of (16), (24), and (40)?
Correct answer: B
Step 1: (16=2^4), (24=2^3\times3), and (40=2^3\times5). Step 2: The common prime factor is (2), and the smallest power is (2^3). Step 3: (2^3=8), so the HCF is (8).
What will be the LCM of (16), (24), and (40)?
Correct answer: C
Step 1: (16=2^4), (24=2^3\times3), and (40=2^3\times5). Step 2: Take the highest powers (2^4), (3), and (5). Step 3: (16\times3\times5=240), so the LCM is (240).
If (a=2^2\times3\times5) and (b=2\times3^2\times5), what is the HCF of (a) and (b)?
Correct answer: B
Step 1: The common prime factors are (2), (3), and (5). Step 2: Their smaller powers are (2), (3), and (5). Step 3: (2\times3\times5=30), so the HCF is (30).
If (a=2^2\times3\times5) and (b=2\times3^2\times5), what is the LCM of (a) and (b)?
Correct answer: C
Step 1: For LCM, take the highest powers of all prime factors. Step 2: The highest powers are (2^2), (3^2), and (5). Step 3: (4\times9\times5=180), so the LCM is (180).
If two numbers are (2^3\times3) and (2^2\times3^2), what will be their HCF?
Correct answer: A
Step 1: The common prime factors are (2) and (3). Step 2: The smaller powers are (2^2) and (3). Step 3: (2^2\times3=12), so the HCF is (12).
If two numbers are (2^3\times3) and (2^2\times3^2), what will be their LCM?
Correct answer: D
Step 1: For LCM, take the highest powers. Step 2: Here the highest powers are (2^3) and (3^2). Step 3: (2^3\times3^2=72), so the LCM is (72).
The HCF of two numbers is (9) and their LCM is (180). What is the product of the two numbers?
Correct answer: C
Step 1: For two numbers, product equals HCF multiplied by LCM. Step 2: (9\times180=1620). Step 3: In such questions, first apply this relation and then multiply carefully.
The HCF of two numbers is (12) and their LCM is (144). What is their product?
Correct answer: B
Step 1: Product of two numbers (=) HCF (\times) LCM. Step 2: (12\times144=1728). Step 3: While multiplying, avoid missing any digit.
If the two numbers are (24) and (36), what is the product of their HCF and LCM?
Correct answer: D
Step 1: For two numbers, HCF (\times) LCM equals the product of the numbers. Step 2: (24\times36=864). Step 3: In such questions, you need not always find HCF and LCM separately.
If the product of two numbers is (720) and their HCF is (12), what will be their LCM?
Correct answer: B
Step 1: Use the relation product (=) HCF (\times) LCM. Step 2: LCM (=\frac{720}{12}=60). Step 3: You can check the answer by multiplying (12) and (60).
If the product of two numbers is (540) and their LCM is (90), what will be their HCF?
Correct answer: B
Step 1: For two numbers, product (=) HCF (\times) LCM. Step 2: HCF (=\frac{540}{90}=6). Step 3: In relation-based questions, place the given values carefully.
QUIZ COMPLETE