LCM of two numbers‌ 

The least common multiple is the smallest of all the multiples which are common in the given numbers.

Multiple

When we multiply a number, for example, we multiply 6 and 4 (not 0), the answer will be 24, meaning 24 is a multiple of 6. Multiples are simply the answers of a multiplication table; if the number comes in a number’s multiplication table, it will be a multiple of that number.
Like, the multiple of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70… and so on.

Common multiple

Many doubts already wither away if you know the meaning of the word ‘common.’ Something present for all or two or more entities have the same things, then that will be common for them. In the same way, if two or more numbers have an exact multiple, then that multiple will be a common multiple for them.
For example, the multiple of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40… and so one
Moreover, the multiple of 8 is 8, 16, 24, 32, 40, 48… and so on.
The common multiples for 4 and 8 are 8, 16, 24, 32, 40…

Least common multiple

The smallest multiple that is common in a particular number for all the given numbers is called the LCM of those numbers.
Example: the multiples of 5 and 10 are
Multiple of 5 – 5, 10, 15, 20, 25, 30, 35, 40, 45, 50…
Multiple of 10 – 10, 20, 30, 40, 50…
The common multiples are 10, 20, 30, 40, 50…
But the least common for 5 and 10 is 10 itself.

Methods to find LCM

• Listing Multiples or Brute Force Method
• Prime Factorization Method
• Division Method or Ladder Method

Listing Multiples or Brute Force Method

In this method, the multiples of each number are written down in a list and then the least common multiple is found.
For example – the LCM 6 and 8
Multiple of 6 – 6,12,18,24,30,36,42,48,54,60…
Multiple of 8 – 8,16,24,32,40,48,56,64,72,80…
The least common multiple in the lists is 24. So, the LCM of 6 and 8 is 24.

Prime Factorization Method

Many people use this method to find LCM. It is the most common method. First, write the prime factors of the number, next multiply each factor on the basis of its occurrence in the number. If the same factor or number occurs multiple times in both numbers, multiply the factor by the maximum number of times it occurs.
For example – the LCM of 6 and 8
6 – 2 x 3
8 – 2 x 2 x 2
2 – three times
3 – one time
LCM = 2 x 2 x 2 x 3 = 24

Division Method or Ladder Method

In this method, two or more numbers are divided with the prime numbers until the division is even. When there are no more prime numbers left that can divide all the numbers, we can multiply the divisors to get the answer.
For example – the LCM of 15 and 24 is
Here, the LCM of 24, 15 will be
= 2 × 2 × 2 × 3 × 5
= 2 x 3 × 3 × 5
= 120