If LCM of a and b is 100 and a + b = 45. Find the difference between a and b.
5
Both a and b must be factors of their LCM 100. Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
We need two factors whose sum is 45: 20 + 25 = 45.
LCM(20, 25): 20 = 2² × 5, 25 = 5², so LCM = 2² × 5² = 100, as required.
Difference = 25 - 20 = 5
Check: 20 + 25 = 45 and LCM(20, 25) = 100.
Hence, 5.
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