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It's easy to find a common multiple of m and n, m × n is a multiple of m and n. m = 2 × 3 × 5 × 5 n = 3 × 5 × 5 × 5 m × n = 2 × 3 × 5 × 5 × 3 × 5 × 5 × 5 The least common multiple of m and n is LCM = 2 × 3 × 5 × 5 × 5 Notice what is different between m × n and the LCM of m and n. The difference is one three and two fives. But 3 × 5 × 5 is the HCF of m and n. So what I see is that
This is true for any positive integers and hence if you know m, n and their LCM you can find their HCF by division. Harley  


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