LCM of two or more numbers is the number that is divisible by all those numbers. In other words, it is the least common multiple of the two or more numbers.
1) Step 1: Find out all factors of numbers
2) Step 2: Take their common factors
3) Step 3: Take their uncommon factors
4) Step 4: Multiply all factors.
5) Step 5: Answer is the LCM of two numbers
Example :
1) Find LCM of 9 and 15
Step 1: Factors of 9 : 3 x 3
Factors of 15 : 3 x 5
Step 2: Common factor is 3 (One 3 is repeated in factors of both the numbers, hence it is common)
Step 3: Uncommon factors are 3 and 5
Step 4: Multiplication of common and uncommon factors = 3 x 3 x 5 = 45
Step 5: Hence LCM of 9 and 15 is 45.
45 is divisible by 9 and 15.
It is the smallest multiple of 9 and 15, hence it is called Least common multiple. Other multiples 9 and 15 are 90, 180.
2. Find LCM of 8 and 12
Step 1: Factors of 8 = 2 x 2 x 2
Factors of 12 = 2 x 2 x 3
Step 2: Common factors are 2,2
Step 3: Uncommon factors are 2,3
Step 4: Multiplication of common and uncommon factors = 2 x 2 x 2 x 3 = 24
Step 5: Hence the LCM of 8 and 12 is 24
Similarly, we can find the LCM of 3 numbers
3. Find LCM of 12, 15, 21
Step 1: Factors of 12 = 2 x 2 x3
Factors of 15 = 3 x 5
Factors of 21 = 3 x 7
Step 2: Common factor is 3
Step 3: Uncommon factors are 2,2,5,7
Step 4: Multiplication of common and uncommon factors = 3 x 2 x 2 x 5 x 7 = 420
Step 5: Hence the LCM of 12, 15 and 21 is 420