# What is the LCM of 3,4 and 6?

LCM of 3, 4 and 6 is the smallest number which divides 3, 4 and 6 exactly without a remainder.

## Answer: LCM of 3, 4 and 6 is 12

## Explanation** **

For 3, 4 and 6 the smallest number which would be perfectly divisible by them is their LCM which is 12. Let us see how to calculate the LCM of 3, 4 and 6 using two methods.

Least Common Multiple of 3, 4 and 6 is the smallest number which will divide 3, 4 and 6 exactly.

### LCM of 3, 4 and 6 by Listing Method

We will list the first few multiples of 3, 4 and 6 and find the common multiples.

- Multiples of 3: 3, 6, 9,
**12**, 15, 18,... - Multiples of 4: 4, 8,
**12**, 16, 20,... - Multiples of 6: 6,
**12**, 18, 24,...

The smallest among the common multiples is the LCM of 3, 4 and 6. So, the LCM of 3, 4 and 6 is 12

### LCM of 3, 4 and 6 by Common Division Method

Here we will divide the numbers 3, 4 and 6 simultaneously with prime numbers until we don't have a prime number to further divide both 3, 4 and 6.PRoduct of the prime numbers used is the LCM of 3 4 and 6.

So, LCM (3, 4, 6) = 2 × 2 × 3 = 12

### Answer: LCM of 3, 4 and 6 is 12