# Problems on LCM

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## Problems on LCM

**Common Multiple: **Defined as number which is exactly divisible by each of the numbers under consideration. **Example **60 is a common multiple of 2,3,4,5,6,10,15,20 and 30

**Lowest Common Multiple(LCM): **LCM of two or more numbers is the least or smallest number which is exactly divisible by each of them.

### Find out LCM of 12, 16

## Solution

Multiples of 12 are 12, 24 ,36, 48, 60
Multiples of 16 are 16, 32, 48, 64
So the least common multiple of both is 48 that is required LCM

### Methods of Finding LCM

### Method of Prime Factors

**Step-1**Resolve each of the given numbers into prime factors**Step-2**Find the product of the highest powers of all the factors that occour in the resolution of the given number. This product will be required LCM

### Find the LCM of 8, 12, 15 and 21

## Solution

8= 2*2*2= 2^3 12= 2*2*3= 2^2*3 15=3*5 21=3*7 So Product of prime numbers with highest powers (2^3)*3*5*7=840 required LCM

### Short Cut Method

Write down the given numbers in a line separating them by commas. Divide by any one of prime numbers 2, 3,5,7 which al least exactly divide at least any two of the given numbers . Repeat down the process untill you get a line of prime numbers. Now the product of all divisors and the numbers in the last line will be the required LCM.

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