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2x2x2x5
The prime factorization of 40 is 2x2x2x5 or 23x5.
The prime factorization of 32 is 2x2x2x2x2 or 25. The prime factorization of 40 is 2x2x2x5 or 23x5. For a number to be a multiple of a given number the multiple must have the entire prime factorization of that number in is. So a multiple of 32 must contain 2x2x2x2x2 or 25 . Likewise a multiple of 40 must contain 2x2x2x5 or 23x5. The least number that this could possible happen with must have 5 factors of 2 and one factor of 5 (the highest exponent on each individual prime factor). Thus the LCM is 2x2x2x2x2x5 or 25x5 Which is 160.
To work this out, you have to split the numbers into the product of their prime factors: 25 = 5x5 40 = 2x2x2x5 The next step is to identify any common factors. In this case, both numbers have a 5 as a prime factor. Thus the HCF of 25 and 40 is 5.
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