Question

What is the GCF and LCM for 30, 35, 36, 42?

Answer 1

They do not have a GCF; their LCM is 1260

Explanation:

If you split each number into it's prime factors then
30 = 2 * 3 * 5
35 = 5 * 7
36 = 2 * 2 * 3 * 3
42 = 2 * 3 * 7

To find the Greatest Common factor you multiply together the lowest power of each prime factor common to all the numbers BUT they do not have any common factors as 35 and 42 have a factor of 7 that is not in 30 or 36
To find the Lowest Common Multiple you multiply together the highest power of each prime factor occurring in any of the numbers, so LCM = 2 * 2 * 3 * 3 *5 * 7 = 1260