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The lcm of two no is 14 times their hcf.the sum of lcm and hcf is 600.if one no is 280,find the other?
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The lcm of two no is 14 times their hcf.the sum of lcm and hcf is 600....
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The lcm of two no is 14 times their hcf.the sum of lcm and hcf is 600....
Problem Statement


Find the other number if one number is 280 and the LCM of two numbers is 14 times their HCF. Also, the sum of LCM and HCF is 600.


Solution


Let the other number be x.


We know that LCM × HCF = product of the two numbers


Given, LCM = 14 × HCF


Therefore, 14 × HCF × HCF = 280 × x


On simplifying, we get:


HCF² = 20 × x/7


Now, we know that LCM + HCF = 600


Substituting LCM = 14 × HCF:


14 × HCF + HCF = 600


15 × HCF = 600


HCF = 40


Using HCF² = 20 × x/7:


40² = 20 × x/7


x = 280 × 49/8 = 1715


Answer


The other number is 1715.
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