Find LCM & HCF

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Q. LCM of 24, 42 and 28

Prime factorizations:

• 24=2³×3


• 42=2×3×7


• 28=2²×7

Take highest powers: 2³,  3¹,  7¹.

LCM = 2³×3×7 = 8×3×7 = 168

Ans: 168

Q. HCF (GCD) of 42, 56 and 63

Prime factorizations:

• 42=2×3×7 


• 56=2³×7


• 63=3²×7

Common prime factors with lowest powers: only 7¹.

HCF = 7.

Ans: 7

Q. LCM of 16a²bc³,  32abc,  64a³bc² 

LCM of 16, 32, 64 = 64

Variables (take the highest powers)

• For a: powers are 2, 1, 3 → highest = 3


• For b: powers are 1, 1, 1 → highest = 1


• For c: powers are 3, 1, 2 → highest = 3

Combine

So

LCM = 64a³b¹c³ 

Ans: 64a³b¹c³

Q. Find the L.C.M. of 4/7,5/21 and 8/63

A. 1/7  B. 1/63 C. 40/63  D. 40/7

Solution:

Formula:

LCM of fractions = LCM of numerators / HCF of denominators

Numerators: 4, 5, 8

LCM(4,5,8) = 40

Denominators: 7, 21, 63

HCF(7,21,63) = 7

Therefore,

LCM = 40/7

Ans: D. 40/7