Problem 27E

What is the least common multiple of each pair in Exercise 25?

Solution:-

Step1

Given that

We have to determine what is the “least common multiple” of the pair in Exercise 24?

Step2

a) 37 · 53 ·73, 211 · 35·59

Definition: - The least common multiple of two integers c and d are the smallest positive integer that is divisible by both c and d.

The positive common multiple of two number is

lcm (lcm=least common multiple)

lcm

Therefore, the least common multiple of each pair of integers is .

Step3

b) 11 · 13· 17, 29 · 37 · 55 · 73

The positive common multiple of two number is

lcm

(lcm=least common multiple)

lcm

Therefore, the least common multiple of each pair of integers is

Step4

c) 2331, 2317

The positive common multiple of two number is

lcm (lcm=least common multiple)

lcm

Therefore, the least common multiple of each pair of integers is .

Step5

d) 41 ·43 · 53, 41 · 43 · 53

The positive common multiple of two number is

lcm (lcm=least common multiple)

lcm

Therefore, the least common multiple of each pair of integers is

Step6

e) 313 · 517, 212 · 721

The positive common multiple of two number is

lcm (lcm=least common multiple)

lcm

Therefore, the least common multiple of each pair of integers is .

Step7

f) 1111, 0

The positive common multiple of two number is

lcm (lcm=least common multiple)

Therefore, the least common multiple of pair of integers is