The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

If a single cook can bake 4 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 4 x 4 = 16 large cakes during that time. 26 large cakes are needed for the party so \( \frac{26}{16} \) = 1\(\frac{5}{8}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 20 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 20 x 4 = 80 small cakes during that time. 420 small cakes are needed for the party so \( \frac{420}{80} \) = 5\(\frac{1}{4}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 2 + 6 = 8 cooks.

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.