# How-To-Solve-LCM Questions Quickly

## How to Solve LCM Questions Quickly

LCM – The least number which is exactly divisible by each one of the given numbers is called their L.C.M.

The least common multiple (LCM) of two or more positive integers is the smallest integer which is a multiple of all of them. Any finite set of integers has an infinite number of common multiples, but only one LCM. The LCM of a set of numbers $\{a_1,a_2,\cdots,a_n\}$ is conventionally represented as $[a_1,a_2,\ldots,a_n]$. ## Type 1:How To Solve LCM Questions Quickly. Find the least or greatest number

### Question 1.

What will be the least number which when doubled will be exactly divisible by 12, 14, 16, 18, and 22?
Options

1. 630
2. 5544
3. 4544
4. 2534

#### Solution

L.C.M. of 12, 14, 16, 18, and 22 = 11088

Required number = (11088 ÷ 2) = 5544

### Question 2

The least number which when divided by 13, 17 and 19 leaves a remainder 10 in each case is?
Options

1. 4209
2. 4290
3. 4029
4. 4902

#### Solution

Required number = (L.C.M of 13, 17, 19) + 10 = 4199 + 10 = 4209

### Question 3

The L.C.M. of two numbers is 40. The numbers are in the ratio 2: 5. Find the sum of the number both the numbers?
Options

1. 26
2. 25
3. 28
4. 120

#### Solution

Let the numbers be 2x and 5x.

Then, their L.C.M. = 10x

So, 10x = 40 or x = 4

Numbers are 2x = 2 * 4 = 8

5x = 5 * 4 = 20

Therefore, required sum = (8 + 20) = 28

## Type 2: How To Solve Quickly LCM Questions. Find LCM

### Question 1

Find the LCM of 16 and 28

Options

1. 121
2. 112
3. 211
4. 120

#### Solution

Prime factorization of 16 = 2 * 2 * 2 * 2 = 24

Prime factorization of 28 = 2 * 2 * 7 = 22 * 71

Highest exponent value we take 24 * 71 = 112

Therefore, LCM (16, 28) = 112

### Question 2

Find the L.C.M of 0.16, 5.4 and 0. 0068

Options

1. 734.4
2. 7344
3. 73.44
4. 7.34

#### Solution

L.C.M (16, 54, 68) = 7344

In numbers 0.16, 5.4, and 0.0098, the minimum digits from right to left are 5.4. Therefore, we

put decimal in our result as 734.4

### Question 3

Find the LCM of two numbers, if the ratio of two numbers is 2: 3 and their HCF is 6.

Options

1. 30
2. 18
3. 40
4. 36

#### Solution

Let the numbers be 2x and 3x

In the question, H.C.F is given as 6

Therefore, the value of x = 6

So the numbers are 2x = 2 * 6 = 12

3x = 3 * 6 = 18

L.C.M. (12, 18) = 36