Find the lowest common multiple of the following
16=2 power of 4
42= 2x3x7
To find the least common multiple (LCM) of the given numbers, we can use their prime factorizations. You have already provided the prime factors for each number:
16 = 2^4 (which means 2 × 2 × 2 × 2)
42 = 2 × 3 × 7
We take the highest power of each prime number that appears in the factorization of both numbers:
- For the prime number 2, the highest power in the given factorizations is 2^4 (from the number 16).
- For the prime number 3, the highest power is 3^1 (from the number 42, as it is the only occurrence of the prime number 3).
- For the prime number 7, the highest power is 7^1 (also from the number 42, as it is the only occurrence of the prime number 7).
Now we can multiply these together to find the LCM:
LCM = 2^4 × 3^1 × 7^1
LCM = 16 × 3 × 7
LCM = 48 × 7
LCM = 336
Therefore, the least common multiple of 16 and 42 is 336.