Question

Find the HCF and LCM of the numbers given below, and verify that their product is equal to the products of the given number
32, 37
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46, 51
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15, 60
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Answer 1

$\Large{\underbrace{\sf{\green{Required \; Solution :}}}}$

Find the HCF and LCM of the numbers given below, and verify that their product is equal to the products of the given number.

✩ 32, 37

        $\Large{ \begin{array}{c|c} \tt 2 & \sf{ 32} \\ \tt 2 & \sf { 16} \\ \tt 2 & \sf{ 8} \\ \tt 2 & \sf{4} \\ \tt 3 & \sf{ 2 }\\ \tt & \sf{ 1 } \end{array}}$         $\Large{ \begin{array}{c|c} \tt 37 & \sf{ 37} \\ \tt & \sf { 1} \end{array}}$

37 & 37 have no common prime factor.

∴ HCF = 1

❍ Verification:-

$\sf{LCM \times HCF = 1184 \times 1 = \underline{1184}} \dots \frak{\orange{(1)}}$

The product of the numbers,

$\implies \sf{32 \times 37}$

$\implies \sf{1184} \dots \frak{\orange{(2)}}$

∴ The product of the HCF and LCM = the product of number.

_

✩ 46, 51

        $\Large{ \begin{array}{c|c} \tt 2 & \sf{ 46} \\ \tt 23 & \sf { 23} \\ \tt & \sf{1}\end{array}}$         $\Large{ \begin{array}{c|c} \tt 3 & \sf{ 51} \\ \tt 17 & \sf { 17} \\ \tt & \sf{1}\end{array}}$

46 & 51 have no common factor.

∴ HCF = 1 & LCM = 46  × 51 = 2341

❍ Verification:-

$\sf{LCM \times HCF = 46 \times 51 = \underline{2341}} \dots \frak{\orange{(1)}}$

The product of the numbers,

∴ The product of the HCF and LCM = the product of number.

_

✩ 15, 60

        $\Large{ \begin{array}{c|c} \tt 3 & \sf{ 15, \; 60} \\ \tt 5 & \sf { 5, \; 20} \\ \tt & \sf{1, \; 4}\end{array}}$

HCF = 3 × 5 = 15

LCM = 3 × 5 × 1 × 4 = 60

$\sf{LCM \times HCF = 15 \times 60 = \underline{900}} \dots \frak{\orange{(1)}}$

The product of the numbers,

$\implies \sf{15 \times 60}$

$\implies \sf{900} \dots \frak{\orange{(2)}}$

∴ The product of the HCF and LCM = the product of number.

__

Apologies for the mistakes! <3

Answer 2

Answer:

900

<3

Step-by-step explanation:

I hope it's helpful

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