What is the HCF of (22) and (33) using prime factorisation?
Correct answer: B
Step 1: (22=2\times11) and (33=3\times11). Step 2: The common prime factor is (11). Step 3: Therefore, the HCF is (11).
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.
25 questions
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Easy · Level 5
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- (1)
- (11)
- (22)
- (33)
Easy · Level 5
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- (55)
- (66)
- (99)
- (132)
Easy · Level 5
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- (3)
- (6)
- (7)
- (14)
Easy · Level 5
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- (120)
- (180)
- (210)
- (420)
Easy · Level 5
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- (14)
- (21)
- (28)
- (42)
Easy · Level 5
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- (84)
- (168)
- (336)
- (672)
Easy · Level 5
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- (9)
- (18)
- (27)
- (36)
Easy · Level 5
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- (216)
- (324)
- (432)
- (972)
Easy · Level 5
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- (15)
- (30)
- (45)
- (90)
Easy · Level 5
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- (45)
- (90)
- (135)
- (180)
Easy · Level 5
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- (6)
- (12)
- (18)
- (24)
Easy · Level 5
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- (72)
- (96)
- (144)
- (288)
Easy · Level 5
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- (5)
- (10)
- (20)
- (25)
Easy · Level 5
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- (350)
- (500)
- (700)
- (1400)
Easy · Level 5
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- (7)
- (14)
- (21)
- (35)
Easy · Level 5
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- (315)
- (420)
- (630)
- (1260)
Easy · Level 5
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- (30)
- (60)
- (90)
- (120)
Easy · Level 5
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- (180)
- (240)
- (360)
- (720)
Easy · Level 5
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- (24)
- (48)
- (72)
- (96)
Easy · Level 5
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- (96)
- (144)
- (288)
- (576)
Easy · Level 5
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- (161)
- (539)
- (1078)
- (2156)
Easy · Level 5
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- (256)
- (1920)
- (3840)
- (4800)
Easy · Level 5
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- (72)
- (84)
- (96)
- (108)
Easy · Level 5
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- (6)
- (9)
- (12)
- (15)
Easy · Level 5
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- (150)
- (2592)
- (5184)
- (10368)
What is the LCM of (22) and (33) using prime factorisation?
Correct answer: B
Step 1: (22=2\times11) and (33=3\times11). Step 2: For LCM, include (2), (3), and (11). Step 3: (2\times3\times11=66), so the answer is (66).
What is the HCF of (30) and (42)?
Correct answer: B
Step 1: (30=2\times3\times5) and (42=2\times3\times7). Step 2: The common prime factors are (2) and (3). Step 3: (2\times3=6), so the HCF is (6).
What is the LCM of (30) and (42)?
Correct answer: C
Step 1: (30=2\times3\times5) and (42=2\times3\times7). Step 2: Take (2), (3), (5), and (7) with highest powers. Step 3: (2\times3\times5\times7=210), so the LCM is (210).
What will be the HCF of (56) and (84)?
Correct answer: C
Step 1: (56=2^3\times7) and (84=2^2\times3\times7). Step 2: The smaller powers of common factors are (2^2) and (7). Step 3: (4\times7=28), so the HCF is (28).
What will be the LCM of (56) and (84)?
Correct answer: B
Step 1: (56=2^3\times7) and (84=2^2\times3\times7). Step 2: The highest powers are (2^3), (3), and (7). Step 3: (8\times3\times7=168), so the answer is (168).
Which is the HCF of (81) and (108)?
Correct answer: C
Step 1: (81=3^4) and (108=2^2\times3^3). Step 2: The common prime factor is (3), and the smaller power is (3^3). Step 3: (3^3=27), so the HCF is (27).
Which is the LCM of (81) and (108)?
Correct answer: B
Step 1: (81=3^4) and (108=2^2\times3^3). Step 2: For LCM, take (2^2) and (3^4). Step 3: (4\times81=324), so the LCM is (324).
What is the HCF of (45) and (90)?
Correct answer: C
Step 1: (45=3^2\times5) and (90=2\times3^2\times5). Step 2: All prime factors of (45) are present in (90). Step 3: Therefore, the HCF is (45).
What is the LCM of (45) and (90)?
Correct answer: B
Step 1: (45=3^2\times5) and (90=2\times3^2\times5). Step 2: The number (90) already contains all factors of (45). Step 3: So the LCM is (90).
What is the HCF of (24), (36), and (48)?
Correct answer: B
Step 1: (24=2^3\times3), (36=2^2\times3^2), and (48=2^4\times3). Step 2: The common smaller powers are (2^2) and (3). Step 3: (4\times3=12), so the HCF is (12).
What is the LCM of (24), (36), and (48)?
Correct answer: C
Step 1: (24=2^3\times3), (36=2^2\times3^2), and (48=2^4\times3). Step 2: The highest powers are (2^4) and (3^2). Step 3: (16\times9=144), so the LCM is (144).
What is the HCF of (20), (50), and (70)?
Correct answer: B
Step 1: (20=2^2\times5), (50=2\times5^2), and (70=2\times5\times7). Step 2: The common factors in all three are (2) and (5). Step 3: (2\times5=10), so the HCF is (10).
What is the LCM of (20), (50), and (70)?
Correct answer: C
Step 1: (20=2^2\times5), (50=2\times5^2), and (70=2\times5\times7). Step 2: The highest powers are (2^2), (5^2), and (7). Step 3: (4\times25\times7=700), so the answer is (700).
What will be the HCF of (42), (63), and (105)?
Correct answer: C
Step 1: (42=2\times3\times7), (63=3^2\times7), and (105=3\times5\times7). Step 2: The common prime factors are (3) and (7). Step 3: (3\times7=21), so the answer is (21).
What will be the LCM of (42), (63), and (105)?
Correct answer: C
Step 1: (42=2\times3\times7), (63=3^2\times7), and (105=3\times5\times7). Step 2: The highest powers are (2), (3^2), (5), and (7). Step 3: (2\times9\times5\times7=630), so the LCM is (630).
If (p=2^2\times3^2\times5) and (q=2^3\times3\times5), what is the HCF of (p) and (q)?
Correct answer: B
Step 1: The common prime factors are (2), (3), and (5). Step 2: The smaller powers are (2^2), (3), and (5). Step 3: (4\times3\times5=60), so the HCF is (60).
If (p=2^2\times3^2\times5) and (q=2^3\times3\times5), what is the LCM of (p) and (q)?
Correct answer: C
Step 1: For LCM, take the highest powers of all prime factors. Step 2: The highest powers are (2^3), (3^2), and (5). Step 3: (8\times9\times5=360), so the answer is (360).
If two numbers are (2^5\times3) and (2^3\times3^2), what will be their HCF?
Correct answer: A
Step 1: The common factors are (2) and (3). Step 2: The smaller powers are (2^3) and (3). Step 3: (2^3\times3=24), so the HCF is (24).
If two numbers are (2^5\times3) and (2^3\times3^2), what will be their LCM?
Correct answer: C
Step 1: For LCM, choose the highest powers. Step 2: Here the highest powers are (2^5) and (3^2). Step 3: (32\times9=288), so the LCM is (288).
The HCF of two numbers is (7) and their LCM is (154). What will be the product of the two numbers?
Correct answer: C
Step 1: For two numbers, product (=) HCF (\times) LCM. Step 2: (7\times154=1078). Step 3: In such questions, knowing the two numbers separately is not necessary.
The HCF of two numbers is (16) and their LCM is (240). What is their product?
Correct answer: C
Step 1: The product of two numbers equals the product of their HCF and LCM. Step 2: (16\times240=3840). Step 3: Writing the relation first reduces calculation mistakes.
If the product of two numbers is (2016) and their HCF is (24), what will be their LCM?
Correct answer: B
Step 1: Use the relation product (=) HCF (\times) LCM. Step 2: LCM (=\frac{2016}{24}=84). Step 3: While dividing, simplify the division carefully.
If the product of two numbers is (2700) and their LCM is (300), what will be their HCF?
Correct answer: B
Step 1: For two numbers, product (=) HCF (\times) LCM. Step 2: HCF (=\frac{2700}{300}=9). Step 3: You can check the answer using (9\times300=2700).
If (54) and (96) are two numbers, what is the product of their HCF and LCM?
Correct answer: C
Step 1: For two numbers, HCF (\times) LCM equals the product of the two numbers. Step 2: (54\times96=5184). Step 3: This shortcut saves time in exams.
QUIZ COMPLETE