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 × b = HCF × LCM Let other number = x. 63 × x = 21 × 693 Compute RHS: 21×693 = 21×(700 − 7) = 14,700 − 147 = 14,553 So x = 14,553 / 63 63×200 = 12,600 Remaining: 1,953 63×30 = 1,890 Remaining: 63 So x = 200 + 30 + 1 = 231 Check: 231 ÷ 21 = 11, So 231 is a multiple of the HCF.
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