Question

1. there is one science lab in the high school. the biology class needs the lab every seventh day of class. the chemistry class needs the lab every fifth day of class. what is the first day the two classes will have a conflict?
2. find the greatest factor for 20, 36, and 48

Explanation:

Step1: Find the least - common multiple for question 4

We need to find the least - common multiple (LCM) of 5 and 7. Since 5 and 7 are prime numbers, their LCM is their product.
$5\times7 = 35$

Step2: Find the greatest common factor for question 5

First, find the prime factorizations of 20, 36 and 48.

• Prime factorization of 20: $20=2^{2}\times5$
• Prime factorization of 36: $36 = 2^{2}\times3^{2}$
• Prime factorization of 48: $48=2^{4}\times3$

The common prime factors are $2^{2}$. So the greatest common factor (GCF) is 4.

Answer:

1. 35
2. 4