Question

Find the L.C.M and H.C.F by prime factorisation method.
a)16,19 and 22
b) 13,23 and 29
c) 9,8 and 18
d)7,6 and 13​

Answer 1

To Find:

• The L.C.M and H.C.F by prime factorisation method.

We know that:

• LCM = Least common multiple
• HCF = Highest common factor

Finding the L.C.M and H.C.F by prime factorisation method:

a) 16, 19 and 22

• Factors of 16 = 2⁴ × 1
• Factors of 19 = 19 × 1
• Factors of 22 = 2 × 11 × 1

LCM = 2⁴ × 19 × 11 = 3344

HCF = 1

Hence,

• LCM of 16, 19 and 22 is 3344.
• HCF of 16, 19 and 22 is 1.

b) 13, 23 and 29

• Factors of 13 = 13 × 1
• Factors of 23 = 23 × 1
• Factors of 29 = 29 × 1

LCM = 13 × 23 × 29 = 8671

HCF = 1

Hence,

• LCM of 13, 23 and 29 is 8671.
• HCF of 13, 23 and 29 is 1.

c) 9, 8 and 18

• Factors of 9 = 3² × 1
• Factors of 8 = 2³ × 1
• Factors of 18 = 2 × 3² × 1

LCM = 3² × 2³ = 72

HCF = 1

Hence,

• LCM of 9, 8 and 18 is 72.
• HCF of 9, 8 and 18 is 1.

d) 7, 6 and 13

• Factors of 7 = 7 × 1
• Factors of 6 = 2 × 3 × 1
• Factors of 13 = 13 × 1

LCM = 7 × 2 × 3 × 13 = 546

HCF = 1

Hence,

• LCM of 7, 6 and 13 is 546.
• HCF of 7, 6 and 13 is 1.

Answer 2

Question:-

Find the L.C.M and H.C.F by prime factorisation method.

a)16,19 and 22

b) 13,23 and 29

c) 9,8 and 18

d)7,6 and 13

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a) L.C.M and H.C.F of 16 , 19 and 22.

$\sf :\implies$ 16 = 2 × 2 × 2 × 2 = 2⁴

$\sf :\implies$ 19 = 19

$\sf :\implies$ 22 = 2 × 11

• L.C.M = 2⁴ × 19 × 11 = 3,344.

• H.C.F = 1

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b) L.C.M and H.C.F of 13 , 23 and 29.

$\sf :\implies$ 13 = 13

$\sf :\implies$ 23 = 23

$\sf :\implies$ 29 = 29

• L.C.M = 13 × 23 × 29 = 8,671.

• H.C.F = 1

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c) L.C.M and H.C.F of 9 , 8 and 18.

$\sf :\implies$ 9 = 3 × 3 = 3²

$\sf :\implies$ 8 = 2 × 2 × 2 = 2³

$\sf :\implies$ 18 = 2 × 9

• L.C.M = 3² × 2³ = 72.

• H.C.F = 1.

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d) L.C.M and H.C.F of 7 , 6 and 13.

$\sf :\implies$ 7 = 7

$\sf :\implies$ 6 = 2 × 3

$\sf :\implies$ 13 = 13

• L.C.M = 2 × 3 × 7 × 13 = 546.

• H.C.F = 1

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