3. the hcf of two numbers is 23 and their lcm is 1449. if one of thenumbers is 161, find the other.

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दो संख्याओं का HCF 23 तथा LCM 1449 है । यदि एक संख्या 161 है तो दूसरी संख्या ज्ञात कीजिए ।

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The HCF of two numbers is 23 and their LCM is 1449 . If one of the numbers is 161 , find the other.

Solution

Let, the two numbers be a and b.

Let the value of a be 161.

Given: HCF = 23 and LCM = 1449

we know, a x b = HCF x LCM

⇒⇒ 161 x b = 23 x 1449

⇒⇒ Therefore, b =

Hence, the other number b is 207

Mathematics

Secondary School Mathematics X

Standard X

The HCF of two numbers is 23 and their LCM is 1449. If one of the numbers is 161, find the other.

Let the two numbers be a and b.Let the value of a be 161.Given: HCF = 23 and LCM = 1449We know, a × b = HCF × LCM                ⇒ 161 × b = 23 × 1449                ⇒ ∴ b =`( 23 ×1449)/161 = 33327/161 = 207`

Hence, the other number b is 207. 

Concept: Euclid’s Division Lemma

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Page 2

The HCF of two numbers is 145 and their LCM is 2175. If one of the numbers is 725, find
the other.

HCF of two numbers = 145LCM of two numbers = 2175Let one of the two numbers be 725 and other be x.Using the formula, product of two numbers = HCF × LCMwe conclude that725 × x = 145 × 2175x = `(145 ×2175)/ 725`= 435

Hence, the other number is 435.

Concept: Euclid’s Division Lemma

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