Short cut the lcm of two numbers is 495 and their hcf is 5. Find the sum if the difference of the number is 10
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Lcm * HCF = a*b ( it is the formula)
Given
LCM (a,b) = 495
HCF(a,b) = 5
LCM(a,b) * HCF (a,b) = a*b
495 * 5 = a*b
2475=ab
given a-b=10
a=10+b--------------------(1)
2475= (10+b)b
2475=10b+b2
b2+10b-2475=0
b2-55b+45b-2475 = 0
b(b-55)+45(b-55)=0
b-55 = 0 and b+45 = 0
b=55 and b=-45
since b cant be negative b=55
a=10+b from (1)
a=10+55
a=65
so the numbers a and b are 65 and 55
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