Question

For each of the following pairs of numbers, show that the product of their HCF and LCM equals their product: (i) 14,21 (ii) 27,90



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Answer 1

Answer:

1)10,15

10=2×5

15=3×5

LCM=2×3×5=30

HCF=5

Hence, LCM×HCF=30×5=150= Product of Numbers

2)35,40

35=5×7

40=2×2×2×5

LCM=5×7×8=280

HCF=5

Hence, LCM×HCF=280×5=1400 = Product of Numbers

3)32,48

32=2×2×2×2×2

48=2×2×2×2×3

LCM=96

HCF=16

Hence, LCM×HCF=96×16=1536 = Product of numbers

Answer 2

Given numbers are:27,90

There LCM-3x3x3x5x2 =270

There HCF=3x3 =9

so, HCF XLCM = product of two numbers 9 x 270 = 27 x 90

2430 2430 Hence proved,

2)35,40

35=5×7

40=2×2×2×5

LCM=5×7×8=280

HCF=5

Hence, LCM×HCF=280×5=1400 = Product of Numbers