The LCM of two numbers is 21 times their HCF. The sum of HCF and LCM of these numbers is 176 .If one of the numbers is 56, find the other number.

Let HCF be x , then LCM = 21 It is given, LCM + HCF = 176 ⇒x + 21x = 176 ⇒ 22x = 176 x = `176/22=` 8 HCF = x = 8 and LCM = 21x = 21 `xx` 8 = 168 Product of two numbers = Product of their HCF and LCM 56 `xx` other number = 8 `xx` 168 Other number =`(8xx168)/56` = 24

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