Question

Find the LCM and HCF of 24, 120 and 144 by using fundamental theorem of Arithmetic.​

Answer 1

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Find the HCF and LCM of 120 and 144 by the fundamental theorem of Arithmetic.

Answer

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Hint:Fundamental theorem of Arithmetic states that every composite number can be factored uniquely as a product of primes. HCF is the highest factor common to two given natural numbers. LCM is the smallest multiple common to two given natural numbers. To find HCF and LCM, first we will find prime factorization of the given natural numbers. Then, observe the common prime factors with smallest power to find HCF and observe all prime factors with greatest power to find LCM.

Complete answer:

First we need to find the prime factorization of given numbers 120 and 144. These both numbers are even so we can start prime factorization with prime numbers 2.

Therefore, 120=2×2×2×3×5=23×31×51

Therefore, 144=2×2×2×2×3×3=24×32

Answer 2

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