Find the lowest common multiple of the following
70=2x5x7
85=5x17
To find the lowest common multiple (LCM) of two numbers, you need to multiply together the highest powers of all the prime numbers that appear in the factorizations of both numbers.
For the numbers 70 and 85, which are factored into primes as follows:
70 = 2 x 5 x 7
85 = 5 x 17
You want to take the prime factors that are unique from each list and the shared factors at their highest powers. In this case:
- For the prime number 2, it appears only in the factorization of 70, so you take 2.
- For the prime number 5, it appears in both numbers, so you take it at its highest power, which is 5^1 (since it is not squared or raised to any higher power).
- For the prime number 7, it appears only in the factorization of 70, so you take 7.
- For the prime number 17, it appears only in the factorization of 85, so you take 17.
Now you multiply all these together to find the LCM:
LCM = 2 x 5 x 7 x 17
Calculating this gives:
LCM = 10 x 7 x 17
LCM = 70 x 17
LCM = 1190
So the lowest common multiple of 70 and 85 is 1190.