What are the Highest common factor and Lowest common multiple of 6, 72, 120 ?
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What are the Highest common factor and Lowest common multiple of 6, 72, 120 ?
Answer: B. 6, 360 — Method: factor each number into primes; HCF is the product of common primes with the smallest exponents, and LCM is the product of all primes with the largest…
- A.
12, 180
- B.
6, 360
- C.
360, 6
- D.
12, 360
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Correct answer: B
Method: factor each number into primes; HCF is the product of common primes with the smallest exponents, and LCM is the product of all primes with the largest exponents.
6 = 2 × 3
72 = 2 × 2 × 2 × 3 × 3 ( = 2^3 × 3^2 )
120 = 2 × 2 × 2 × 3 × 5 ( = 2^3 × 3 × 5 )
HCF calculation: common primes are 2 and 3 with minimum exponents 1 and 1 → HCF = 2 × 3 = 6
LCM calculation: take the highest exponents for each prime: 2^3, 3^2, 5^1 → LCM = 2 × 2 × 2 × 3 × 3 × 5 = 360
Final answer: HCF = 6, LCM = 360