What is the LCM of (63) and (84)?
Correct answer: C
Step 1: (63=3^2\times7) and (84=2^2\times3\times7). Step 2: The highest powers are (2^2), (3^2), and (7). Step 3: (4\times9\times7=252), so the LCM is (252).
View question detailsMathematics
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.
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Easy · Level 10 · real-numbers,lcm,prime-factorisation
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- (126)
- (168)
- (252)
- (504)
Easy · Level 10 · real-numbers,hcf,given-factorisation
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- (12)
- (24)
- (36)
- (48)
Easy · Level 10 · real-numbers,lcm,given-factorisation
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- (240)
- (360)
- (480)
- (960)
Easy · Level 10 · real-numbers,hcf,three-numbers
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- (5)
- (10)
- (20)
- (25)
Easy · Level 10 · real-numbers,lcm,three-numbers
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- (100)
- (200)
- (400)
- (500)
Easy · Level 10 · real-numbers,hcf,prime-factorisation
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- (11)
- (22)
- (33)
- (44)
Easy · Level 10 · real-numbers,lcm,prime-factorisation
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- (132)
- (264)
- (528)
- (1056)
Easy · Level 10 · real-numbers,prime-factorisation,basic
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- (42)
- (56)
- (84)
- (126)
Easy · Level 10 · real-numbers,prime-factorisation,basic
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- (100)
- (200)
- (250)
- (400)
Easy · Level 10 · real-numbers,hcf,co-prime-concept
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- They are co-prime
- They are always equal
- Their LCM is (1)
- Both are always prime
Easy · Level 10 · real-numbers,hcf,concept
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- Smaller power of common factors
- Highest power of all factors
- Only uncommon factors
- Sum of all factors
Easy · Level 11 · real-numbers,hcf,prime-factorisation
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- (5)
- (10)
- (15)
- (20)
Easy · Level 11 · real-numbers,lcm,prime-factorisation
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- (30)
- (40)
- (60)
- (120)
Easy · Level 11 · real-numbers,hcf,class-10
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- (7)
- (14)
- (21)
- (28)
Easy · Level 11 · real-numbers,lcm,class-10
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- (56)
- (84)
- (126)
- (168)
Easy · Level 11 · real-numbers,hcf,prime-powers
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- (9)
- (12)
- (18)
- (27)
Easy · Level 11 · real-numbers,lcm,prime-powers
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- (54)
- (72)
- (108)
- (216)
Easy · Level 11 · real-numbers,hcf,prime-factorisation
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- (11)
- (22)
- (33)
- (44)
Easy · Level 11 · real-numbers,lcm,prime-factorisation
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- (66)
- (88)
- (132)
- (264)
Easy · Level 11 · real-numbers,hcf,square-number
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- (5)
- (7)
- (10)
- (14)
If (96=2^5\times3) and (120=2^3\times3\times5), what is their HCF?
Correct answer: B
Step 1: The common prime 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).
View question detailsIf (96=2^5\times3) and (120=2^3\times3\times5), what is their LCM?
Correct answer: C
Step 1: The LCM contains the highest powers of all prime factors. Step 2: The highest powers are (2^5), (3), and (5). Step 3: (32\times3\times5=480), so the answer is (480).
View question detailsWhat is the HCF of (25), (40), and (50)?
Correct answer: A
Step 1: (25=5^2), (40=2^3\times5), and (50=2\times5^2). Step 2: The common prime factor in all three numbers is (5). Step 3: The smallest power is (5), so the HCF is (5).
View question detailsWhat is the LCM of (25), (40), and (50)?
Correct answer: B
Step 1: (25=5^2), (40=2^3\times5), and (50=2\times5^2). Step 2: The highest powers are (2^3) and (5^2). Step 3: (8\times25=200), so the LCM is (200).
View question detailsWhat is the HCF of (88) and (132)?
Correct answer: D
Step 1: (88=2^3\times11) and (132=2^2\times3\times11). Step 2: The smaller powers of common factors are (2^2) and (11). Step 3: (4\times11=44), so the HCF is (44).
View question detailsWhat is the LCM of (88) and (132)?
Correct answer: B
Step 1: (88=2^3\times11) and (132=2^2\times3\times11). Step 2: The highest powers are (2^3), (3), and (11). Step 3: (8\times3\times11=264), so the LCM is (264).
View question detailsThe prime factorisation of a number is (2^2\times3\times7). What is the number?
Correct answer: C
Step 1: First simplify the given prime powers. Step 2: Since (2^2=4), the number is (4\times3\times7=84). Step 3: Reading prime factorisation correctly helps in HCF and LCM questions.
View question detailsThe prime factorisation of a number is (2^3\times5^2). What is the number?
Correct answer: B
Step 1: (2^3=8) and (5^2=25). Step 2: Multiplying them gives (8\times25=200). Step 3: Always simplify powers first and then multiply.
View question detailsIf the HCF of two numbers is (1), which statement about them is correct?
Correct answer: A
Step 1: If the HCF of two numbers is (1), they have no common factor except (1). Step 2: Such numbers are called co-prime. Step 3: Co-prime numbers need not both be prime numbers.
View question detailsIn the prime factorisation method for finding HCF, which power is chosen?
Correct answer: A
Step 1: HCF is made only from common prime factors. Step 2: Among common factors, the smaller power is chosen because it divides both numbers. Step 3: Remember the rule: common factors with smaller powers for HCF.
View question detailsWhat is the HCF of (20) and (30) using prime factorisation?
Correct answer: B
Step 1: (20=2^2\times5) and (30=2\times3\times5). Step 2: The common prime factors are (2) and (5) with smaller powers (2) and (5). Step 3: (2\times5=10), so the HCF is (10).
View question detailsWhat is the LCM of (20) and (30) using prime factorisation?
Correct answer: C
Step 1: (20=2^2\times5) and (30=2\times3\times5). Step 2: For LCM, take the highest powers (2^2), (3), and (5). Step 3: (4\times3\times5=60), so the LCM is (60).
View question detailsWhat is the HCF of (28) and (42)?
Correct answer: B
Step 1: (28=2^2\times7) and (42=2\times3\times7). Step 2: The common factors are (2) and (7). Step 3: (2\times7=14), so the HCF is (14).
View question detailsWhat is the LCM of (28) and (42)?
Correct answer: B
Step 1: (28=2^2\times7) and (42=2\times3\times7). Step 2: The highest powers are (2^2), (3), and (7). Step 3: (4\times3\times7=84), so the LCM is (84).
View question detailsWhat will be the HCF of (36) and (54)?
Correct answer: C
Step 1: (36=2^2\times3^2) and (54=2\times3^3). Step 2: The smaller powers of common factors are (2) and (3^2). Step 3: (2\times9=18), so the HCF is (18).
View question detailsWhat will be the LCM of (36) and (54)?
Correct answer: C
Step 1: (36=2^2\times3^2) and (54=2\times3^3). Step 2: For LCM, take the highest powers (2^2) and (3^3). Step 3: (4\times27=108), so the answer is (108).
View question detailsWhich is the HCF of (44) and (66)?
Correct answer: B
Step 1: (44=2^2\times11) and (66=2\times3\times11). Step 2: The common prime factors are (2) and (11). Step 3: (2\times11=22), so the HCF is (22).
View question detailsWhich is the LCM of (44) and (66)?
Correct answer: C
Step 1: (44=2^2\times11) and (66=2\times3\times11). Step 2: Take the highest powers (2^2), (3), and (11). Step 3: (4\times3\times11=132), so the LCM is (132).
View question detailsWhat is the HCF of (49) and (70)?
Correct answer: B
Step 1: (49=7^2) and (70=2\times5\times7). Step 2: The only common prime factor is (7). Step 3: Therefore, the HCF is (7).
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