Divide the first number by the lowest prime number applicable, usually 2. Prime numbers are infinite and include 2, 3, 5, 7, 11, 13, 17 and 19. Start by dividing the first number by 2. If it isn't divisible by 2, try 3, then 5. Keep doing this until you find a number that works. For example, the number 524 is divisible by 2, resulting in 262. Express this new value as 2 x 262.
Continue dividing the number by the lowest prime number possible. The number 262 is also divisible by 2, resulting in 131. This is a prime number and cannot be divided any further.
Write the prime factorization by listing all prime numbers used in multiplying to arrive at the original number. The prime factorization of 524 is 2 x 2 x 131.
Repeat for the second number. Every number has a unique prime factorization and must be calculated individually. For example, the prime factorization of 420 is 2 x 2 x 3 x 5 x 7. You can now compare the prime factorization of 524 and 420 to determine other values, such as the greatest common factor, or GCF. This is the largest factor that both numbers can be divided by. The GCF for 524 and 420 is 2 x 2, or 4.
Use the prime factorization to determine the relative primes of the two numbers, which is the prime numbers that are included in the prime factorization breakdown of both numbers. The only relative prime number for 524 and 420 is 2 because 2 is the only prime number that occurs in both prime factorizations.
Use prime factorization to determine the least common multiple, the smallest number that can be divided by both of the original numbers. Multiply the two numbers, then divide the total by the GCF. Multiplying 524 by 420 equals 220,080. Divide this by the GCF of 4 to get 55,020. The least common multiple of 540 and 420 is 55,020.