+90 What is the LCM of 8, 12, and 16. Plz show your work too
+223 The LCM is the smallest number that is divisible by 8, 12, and 16.
To find it, I would suggest listing a few multiples of the highest number and seeing if 8 and 12 go into those multiples.
A few multiples of 16 would be: 16, 32, 48, 64
Now we can check if 8 or 12 go into any of those.
8 goes into 16, 32, 48, and 64 but 12 only goes into 48.
Therefore 48 is the LCM.
Find the least common multiple:
lcm(8, 12, 16)
Find the prime factorization of each integer:
The prime factorization of 8 is:
8 = 2^3
The prime factorization of 12 is:
12 = 2^2×3
The prime factorization of 16 is:
16 = 2^4
Find the largest power of each prime factor.
The largest power of 2 that appears in the prime factorizations is 2^4.
The largest power of 3 that appears in the prime factorizations is 3^1.
Therefore lcm(8, 12, 16) = 2^4×3^1:
Answer: |lcm(8, 12, 16) = 48
