What is the lowest possible integer that is divisible by each of the integers…

Solution: Find the least common multiple (LCM) of 1 through 7 by taking the highest power of each prime that appears in their factorizations.

• Prime factorizations to consider: 2 = 2, 3 = 3, 4 = 2^2, 5 = 5, 6 = 2 * 3, 7 = 7

• Take the highest powers of each prime that appear: 2^2 (from 4), 3^1 (from 3 or 6), 5^1, 7^1

• Compute the LCM: 2^2 * 3 * 5 * 7 = 4 * 3 * 5 * 7 = 420

• Therefore, the smallest integer divisible by each of the integers 1 through 7 is 420.