# Least Common Multiple

Step by step explanation of finding Least Common Factor (LCM) of numbers by Least Common Multiple Method, Prime Factorisation Method, Tree Method and Ladder Method.

Least common multiple-

Least common multiple of two or more non zero positive numbers is a least common multiples of all numbers.

Methods to find out least common multiple

(1)Finding multiples method-

Eg:-

Find least common multiple of 4 and 3

Step 1-

Write multiples of 3

Multiples of 3 = 3,6,9,12,15,18,21,24

Step 2-

Write multiples of 4

Multiples of 4 = 4,8,12, 16,20,24,28

Step 3-

Find least common multiple.

Here, 12 is a least common multiple of 3 and 4.

Eg:-

Find least common multiple of 4, 3 and 2

Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 1 8

Multiples of 3 = 3,6,9,12,15,18,21,24

Multiples of 4 = 4,8,12, 16,20,24,28

12 is a least common multiple of 3, 4 and 2.

(2)Prime factorisation method

Eg:-

Find the LCM of 16, 18 and 25

Step 1-

Write prime factors of 16

Prime factorisation of 16 = 2 × 2 × 2 × 2

Step 2-

Write prime factor of 18

Prime factorisation of 18 = 2 × 3 × 3

Step 3-

Write prime factor of 25

Prime factorization of 25 = 5 × 5

Step 4-

Find common prime factors

Common prime factor of 16 and 18 = 2

Step 5-

Now, write common factor and other factors .Multiply them to get LCM.

LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5

Here, 2 is a common factor. Therefore, 2 will come four times (one time 2 as common factor and three times 2 as non-common factor) to make 16 . Two time 3 and one time common factor 2 will make 18. 25 dose not has any common factor so all factors of it will include in calculating LCM.

LCM = 3600

(3) Tree method-

Eg:- Find the least common multiple of 45 and 25.

Ans-

Prime factorisation of 45   Eg:- Find the LCM of 45 and 25

Step1:-

Do prime factorisation of both numbers by prime numbers. Both numbers can be divided exactly (no remainder).

Step2:-

Now, multiply all the factors and quotients, we will get least common multiple (LCM). LCM = 5 × 3 × 3 × 5 = 225

Hence, LCM of given numbers is 225.

Helping Topics

NCERT Solutions Class 7

Worksheet Class 7