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# Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = Product of the two numbers. 1) 26 and 912) 510 and 923) 336 and 54

1.26 and 91
$$26 = 2 × 13$$
$$91 = 7 × 13$$
HCF = 13
LCM = $$2 × 7 × 13 = 182$$

Product of two numbers 26 and 91 = $$26 × 91 = 2366$$
HCF × LCM = $$13 × 182 = 2366$$

Product of two numbers is HCF × LCM, so it is verified.

2.510 and 92
$$510 = 2 × 3 × 5 × 17$$
$$92 = 2 × 2 × 23$$
HCF = 2
LCM = $$2 × 2 × 3 × 5 × 17 × 23 = 23460$$

Product of two numbers 510 and 92 = $$510 × 92 = 46920$$
HCF × LCM = $$2 × 23460 = 46920$$

Product of two numbers is HCF × LCM, so it is verified

3.336 and 54
$$336 = 2 × 2 × 2 × 2 × 3 × 7 = 2^4 + 3 + 7$$
$$54 = 2 × 3 × 3 × 3 = 2 × 3^3$$
HCF = $$2 × 3 = 6$$
LCM = $$2^4 × 3^3 × 7 = 3024$$

Product of two numbers 336 and 54 = $$336 × 54 = 18144$$
HCF × LCM = $$6 × 3024 = 18144$$

Product of two numbers is HCF × LCM, so it is verified.