Question

What is LCM?
Various method of finding LCM​

Answer 1

Answer:

Meaning of LCM is least common multiple

Lowest common multiple or smallest common multiple of two integers a and b usually denoted by LCM (a,b) is the smallest positive integer that is divisible by both a and b

Step-by-step explanation:

Various....Methods.....

• One way to find the least common multiple of two numbers is to first list the prime factors of each number. Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs

Answer 2

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Least Common Multiple (LCM) is a way of finding the smallest common multiple between any two numbers or more. A common multiple is a multiple of two numbers or more. LCM denotes the less common or multiple factors of any two or more given integers.

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• Brute Force method

In this method, the multiples of each number are listed until the first common multiple is found.

Example: Calculate the LCM of 16 and 20.

Answer:

Let us consider

The multiples of 16 = 16, 32, 48, 64, 80,…..

The multiple of 20 = 20, 40, 60, 80,……

The first common multiple for both the numbers is 80.

So LCM of 16 and 20 is 80.

Prime Factorization method

The prime factorization is one of the most common ways of finding LCM.

Example: Calculate the LCM of 30 and 45.

Answer:

Let us calculate the prime factors of two number

30 = 2 × 3 × 5

45 = 3 × 3 × 5

Multiply each factor the maximum number of times it occurs in either number.

LCM = 2 × 3 × 3 × 5

LCM = 90

• Ladder method

In this method, the two numbers are simultaneously divided with prime numbers until the division is even. When there are no more primes that evenly divide into both numbers, multiply the divisors to get the LCM.

GCF (Greatest Common Factor) method

The method is used only when the GCF of two numbers is given. The formula used to find the LCM is

L.C.M. = a × b/ gcd (a, b)

Example: Calculate the LCM of 15 and 24. GCF given is 3.

Answer:

Answer:LCM (15 × 24) / 3

Answer:LCM (15 × 24) / 3LCM = 3.