L.C.M:
The smallest number that is a common multiple of the provided numbers is known
as the least common multiple (LCM).
How to Find HCF and LCM?Finding the HCF and LCM of numbers can be done in a number of ways. The following are the most widely used techniques:– Prime factorization method– Division method
By prime factorization, we may find the HCF of any given set of numbers. We determine the product of the prime factors that are common to all of the given numbers after we've found the factors.
Example: Find H.C.F of 24 and 36. Here,
The prime factors of
24 = 2 × 2 ×2 x 3
The prime factors of
36 = 2 ×2 × 3 x 3
The common factors of 24 and 36 are 2 x2 x3.
Thus, HCF of (24, 36) = 12
LCM by Prime Factorization:The LCM of the supplied numbers is equal to the product of the numbers common prime factors and uncommon prime factors.
Example: Let's use prime factorization to find the LCM of 24 and 36.
The prime factors of
24 = 2 × 2 × 2 × 3 and
36 = 2 × 2 × 3 ×3.
The product of all the prime factors = Common prime factors (2 ×2 x 3 )× Uncommon prime factors (2 × 3).Therefore, LCM of 24 and 36 = 12*6 = 72.
HCF and LCM Techniques:• If 1 is the HCF of two numbers, then the product is their LCM.
HCF and LCM Techniques:2. The HCF for two co prime numbers is always 1