# How-To-Solve LCM & HCF Questions Quickly

## How to Solve Quickly HCF Questions

HCF – Highest Common Factor (HCF) of two or more numbers is the greatest number which divides each of them exactly.

## How to Solve Quickly LCM Questions

LCF – Least Common Factor is a least number that divide any number and leaves remainder zero. ## Type 1: Find the greatest or smallest number.

### Question 1.

The greatest possible length which can be used to measure exactly the lengths 5 m, 4 m, 12 m 55 cm is

Options

1. 2
2. 10
3. 25
4. 5

#### Solution:

H.C.F. of (500 cm, 400 cm, 1255 cm) = 5 cm

The factors of 400 are: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400

The factors of 500 are: 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500

The factors of 1255 are: 1, 5, 251, 1255

Then the highest common factor is 5

### Question 2.

The H.C.F. and L.C.M. of two numbers are 10 and 5040 respectively. If one of the numbers is 175, find the other number?

Options

1. 288
2. 300
3. 308
4. 280

#### Solution:

We know that, Product of two numbers = H.C.F x L.C.M

175 x a = 10 x 5040

Therefore, a (10 * 5040)/175 = 50400/175 = 288

So, the other number = 288

### Question 3.

Find the greatest number which on dividing 1484 and 2045 leaves remainders 4 and 5 respectively?

Options

1. 20
2. 30
3. 10
4. 40

#### Solution:

Required number = H.C.F. of (1484 – 4) and (2045 – 5)

= H.C.F. of 1480 and 2040 = 40

## Type 2: How to Solve LCM and HCF Questions Quickly.Find HCF

### Question 1.

Three numbers are in the ratio of 4: 3: 6 and their L.C.M. are 3600. Find their H.C.F:

Options

1. 20
2. 30
3. 10
4. 40

#### Solution:

Let the numbers be 4x, 3x and 6x

Then, their L.C.M. = (4x * 3x *6x) = 72x

So, 72x = 3600 or x = 50

Therefore, numbers are (4 x 50), (3 x 50) and (6 x 30) = 200, 150, 180

The factors of 150 are: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

The factors of 180 are: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

The factors of 200 are: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200

Then the highest common factor is 10.

Hence, required H.C.F. = 10

### Question 2.

Find the HCF of 34, 48, 56, and 74

Options

1. 2
2. 4
3. 34
4. 8

#### Solution:

The factors of 34 are: 1, 2, 17, 34

The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56

The factors of 74 are: 1, 2, 37, 74

Therefore, the highest common factor is 2.

### Question 3.

Find the HCF of 2/11, 4/17, 6/5

Options

1. 1/935
2. 2/935
3. 2/93
4. 2/35

#### Solution:

We know that

HCF = HCF of Numerator/LCM of Denominators

HCF = HCF (2, 4, 6)/ LCM (11, 17, 5)

HCF = 2/935