two numbers are in the ratio 2:3 if there LCM is 108 then HCM?
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Two numbers are in ratio 3:4, their LCM is 108. What is their HCF?
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10 Answers

Yashima Arora, former Business Technology Analyst at Deloitte (2017-2019)
Answered 27 June 2019
As the numbers are given in a ratio, take the no. as 3x and 4x (as x is common)
LCM - Least Common Multiple or highest power of each prime factor
108 = 2^2 * 3^3
3X = 3^X
4X = 2^2 *X
Now finding LCM from these no. should include highest power of each prime factor - which is 2^2 and 3^3. This means X should be 3^2 which is missing for LCM to be 108.
Hence, the HCF - Highest Common factor or the lowest matching power of prime factors is 3^2 = 9
The two numbers are - 27 (3^3) and 36 (2^2 * 3^2)
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