Find the Least Common Multiple (LCM) of 40 and 15.
To find the least common multiple (LCM) of 40 and 15, you can start by factoring the two numbers:
40 = 2 x 2 x 2 x 5 = 2^3 x 5
15 = 3 x 5
Next, you need to find the highest power for each prime factor:
The highest power of 2 is 3 (from 40) and the highest power of 3 is 1 (from 15).
The highest power of 5 is 1 (from both 40 and 15).
Finally, multiply all the prime factors with the highest powers:
2^3 x 3^1 x 5^1 = 8 x 3 x 5 = 120
Therefore, the LCM of 40 and 15 is 120.