Prime factorization of 160 in exponential form is 25 x 5.
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The prime factorization, using exponents, of 160 is: 25 x 5
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.
160 = 2 x 2 x 2 x 2 x 2 x 5
2 x 2 x 2 x 2 x 2 x 5 = 160
160 is even so it's divisible by 2 160/2=80.....so far we have a 2 80 is even again, 80/2=40 now we have 2^2 40/2 = 20 we have 2^3 20/2 = 10 ...2^4 10/2= 5 ... 2^5 5 is prime so the prime factorization of 160 is 2^5 *5