Question

For each of the following pairs of numbers, verify that product of numbers is
equal to the product of their HCF and LCM.
(a) 10. 15
(b) 35. 40
(c) 32, 48​

Answer 1

Step-by-step explanation:

By prime factorization method:

(a)10=2×5

15=3×5

HCF=5

LCM=2×3×5=30

product of the numbers=10×15=150

HCF×LCM=30×5=150

150=150

Hence product of the numbers=HCF×LCM

(b)By prime factorization method:

(b)35=5×7

40=2×2×2×5

HCF=5

LCM=5×7×2×2×2=280

product of the numbers=35×40=1400

HCF×LCM=5×280=1400

1400=1400

Hence product of the numbers=HCF×LCM

(c)By prime factorization method:

32=2×2×2×2×2

48=2×2×2×2×3

HCF=16

LCM=2×2×2×2×2×3=96

product of the numbers=32×48=1536

HCF×LCM=16×96=1536

1536=1536

Hence product of the numbers=HCF×LCM

I hope this answer may help you

Answer 2

Step-by-step explanation:

$\huge\purple{Answer:-\:}\downarrow$

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

HOPE IT HELPS YOU!

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