Find the least common multiple:
lcm(20, 40, 30)
Find the prime factorization of each integer:
The prime factorization of 20 is:
20 = 2^2×5
The prime factorization of 40 is:
40 = 2^3×5
The prime factorization of 30 is:
30 = 2×3×5
Find the largest power of each prime factor.
The largest power of 2 that appears in the prime factorizations is 2^3.
The largest power of 3 that appears in the prime factorizations is 3^1.
The largest power of 5 that appears in the prime factorizations is 5^1.
Therefore lcm(20, 40, 30) = 2^3×3^1×5^1:
Answer: | lcm(20, 40, 30) = 120
