Question

Show that the product of two numbers 60 and.84 is equal to the product of their HCF and LCM

Answer 1

Prime factorisation of $60=2\times 2\times 3\times 5$
Prime factorisation of $84=2\times 2\times 3\times 7$
Hence, LCM of $60,84=2\times 2\times 3\times 5\times 7=420$
And HCF of $60,84=2\times 2\times 3=12$
Now, LCM $\times$ HCF $=420\times 12=5040$
Also, $60\times 84=5040$
i.e., HCF $\times$ LCM $=$ Product of the two numbers