# Chapter 1 - Some Basic Concepts of Arithmetic and Algebra - 1.2 - Prime and Composite Numbers - Problem Set 1.2 - Page 14: 90

840

#### Work Step by Step

Finding the least common multiple of 2, 3, 4, 5, 6, 7, and 8 can be done using prime factorization, as follows: 1. Factor each number into primes (for example, 6 becomes 2 x 3). 2. For each prime, find the factor where it occurs the most (for example, the prime number 2 occurs the most in the factor of 8, which is 2 x 2 x 2). 3. Multiply the factors where the primes occur the most to find the LCM. In this case, the factors with the most primes were (2 x 2 x 2) from 8, (3) from 3, (5) from 5, and (7) for 7. (2 x 2 x 2 x 3 x 5 x 7) is equal to 840.

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