HOW TO FIND HCF AND LCM EASILY

Example 1 :

Find the HCF and LCM of 90 and 30.

Solution :

Decompose 90 and 30 into prime factors using ladder method.

HCF of (90, 30) :

= 2 x 3 x 5

= 30

LCM of (90, 30) :

= 2 x 3 x 5 x 3 x 1

= 90

Example 2 :

Find the HCF and LCM of 105 and 60.

Solution :

Decompose 105 and 60 into prime factors using ladder method.

HCF of (105, 60) :

= 2 x 3 x 5

= 30

LCM of (105, 60) :

= 3 x 5 x 7 x 4

= 420

Example 3 :

Find the HCF and LCM of 30 and 50.

Solution :

Decompose 30 and 50 into prime factors using ladder method.

HCF of (30, 50) :

= 5 x 2

= 10

LCM of (30, 50) :

= 5 x 2 x 3 x 5

= 150

Example 4 :

Find the HCF and LCM of 80 and 60.

Solution :

Decompose 80 and 60 into prime factors using ladder method.

HCF of (80, 60) :

= 5 x 2 x 2

= 20

LCM of (80, 60) :

= 5 x 2 x 2 x 4 x 3

= 240

Example 5 :

Find the HCF and LCM of 36 and 27.

Solution :

Decompose 36 and 27 into prime factors using ladder method.

HCF of (36, 27) :

= 3 x 3

= 9

LCM of (36, 27) :

= 3 x 3 x 4 x 3

= 108

Example 6 :

Find the HCF and LCM of 75 and 45.

Solution :

Decompose 75 and 45 into prime factors using ladder method.

HCF of (75, 45) :

= 5 x 3

= 15

LCM of (75, 45) :

= 5 x 3 x 5 x 3

= 225

Example 7 :

Find the HCF and LCM of 36 and 72.

Solution :

Decompose 36 and 72 into prime factors using ladder method.

HCF of (36, 72) :

= 2 x 2 x 3 x 3

= 36

LCM of (36, 72) :

= 2 x 2 x 3 x 3 x 1 x 2

= 72

Example 8 :

Find the HCF and LCM of 72 and 63.

Solution :

Decompose 72 and 63 into prime factors using ladder method.

HCF of (72, 63) :

= 3 x 3

= 9

LCM of (72, 63) :

= 3 x 3 x 8 x 7

= 504

Example 9 :

Find the HCF and LCM of 120 and 90.

Solution :

Decompose 120 and 90 into prime factors using ladder method.

HCF of (120, 90) :

= 3 x 2 x 5

= 30

LCM of (120, 90) :

= 3 x 2 x 5 x 4 x 3

= 360

Example 10 :

Find the HCF and LCM of 45 and 135.

Solution :

Decompose 45 and 135 into prime factors using ladder method.

HCF of (45, 135) :

= 5 x 3 x 3

= 45

LCM of (45, 135) :

= 5 x 3 x 3 x 1 x 3

= 135

Example 11 :

Find the HCF and LCM of 28, 42 and 56.

Solution :

Decompose 28, 42 and 56 into prime factors using ladder method.

HCF of (28, 42, 56) :

= 2 x 7

= 14

LCM of (28, 42, 56) :

= 2 x 7 x 2 x 1 x 3 x 2

= 168

Example 12 :

Find the HCF and LCM of 45, 55 and 95.

Solution :

Decompose 45, 55 and 95 into prime factors using ladder method.

HCF of (45, 55, 95) :

= 5

LCM of (45, 55, 95) :

= 5 x 9 x 11 x 19

= 9405

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