Sample Material SSC CGL TIER-2 Online Coaching

Numerical Aptitude (Chapter - HCF & LCM)

Highest Common Factor

The highest common factor of two or more given numbers is the largest of their common factors. It is known as GCD also. eg, Factors of 20 are 1, 2, 4, 5, 10, 20

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36

Here greatest and common factor of 20 and 36 is 4.

HCF of 20 and 36 is 4.

Least Common Multiple

The least common multiple of two or more given numbers is the least of their common multiples. eg, Multiple of 25 are 25, 50, 75, 100, 125, 150, 175, ....

Multiple of 30 are 30, 60, 90, 120, 150, 180, 210, ....

Here 150 is least common multiple of 25 and 30

LCM of 25 and 30 is 150.

Using Division Method

Example 1: Determine the HCF and LCM of 36, 48, 64 and 72.

Solution. To find HCF

therefore, HCF of 36, 48, 64 and 72 is 4.

To find LCM

To determine LCM of 14, 42, 21.

HCF and LCM of Fractions

HCF of fraction = (HCF of Numerators) / (LCM of Denominators)

LCM of fraction = (LCM of Numerators) / (HCF of Denominators)

:: Home Assignment for Practice ::

1. How many numbers less than 10,000 are there which are divisible by 21, 35 and 63?

(a) 33
(b) 32
(c) 38
(d) 31

2. Find the side of the largest possible square slabs which can be paved on the floor of a room 2m 50 cm long and 1 m 50 cm broad. Also find the number of such slabs to pave the floor.

(a) 40, 18
(b) 30, 15
(c) 50, 15
(d) 20, 25

3. What is the largest number which when divides 1475, 3155 and 5255 leaves the same remainder in each case?

(a) 220
(b) 420
(c) 350
(d) 540

4. A florist has 200 roses and 180 jasmines with him. He was asked to make garlands of flowers with only roses or only jasmines each containing the same number of flowers. What will be the largest number of flowers, he can join together without leaving a single flower?

(a) 16
(b) 17
(c) 20
(d) 19

5. The HCF and LCM of a pair of numbers are 12 and 926 respectively. How many such distinct pairs are possible?

(a) 3
(b) 7
(c) 1
(d) 0

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