Question
The HCF of two numbers is 21 and their LCM is 693. If
one of the numbers is 63, find the other number and verify that it is a multiple of the HCF.Solution
For two numbers a and b: a Γ b = HCF Γ LCM Let other number = x. 63 Γ x = 21 Γ 693 Compute RHS: 21Γ693 = 21Γ(700 β 7) = 14,700 β 147 = 14,553 So x = 14,553 / 63 63Γ200 = 12,600 Remaining: 1,953 63Γ30 = 1,890 Remaining: 63 So x = 200 + 30 + 1 = 231 Check: 231 Γ· 21 = 11, So 231 is a multiple of the HCF.