Greatest Common Factor and Least Common Multiple

Math ⇒ Number and Operations

Greatest Common Factor and Least Common Multiple starts at 6 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Greatest Common Factor and Least Common Multiple. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 12

A factory produces two products, one every 18 minutes and the other every 24 minutes. If both products are started at the same time, after how many minutes will both be produced together again?

A teacher wants to arrange 60 red pens and 84 blue pens in equal groups with no pens left over. What is the greatest number of groups possible?

Explain how the prime factorization of two numbers can be used to find their GCF and LCM.

Explain the difference between the greatest common factor and the least common multiple.

Find the GCF and LCM of 105 and 168.

Find the GCF of 2³ × 3² × 5 and 2² × 3 × 7.

Find the greatest common factor (GCF) of 84 and 126.

Find the LCM of 15, 20, and 30.

Find the LCM of 2⁴ × 3 and 2² × 3³.

Find the LCM of 45, 60, and 75.

Given the numbers 36 and 48, what is their GCF and LCM?

If the GCF of two numbers is 1, what are these numbers called?

If the GCF of two numbers is 8 and their LCM is 120, what could be the two numbers?

If the LCM of two numbers is 180 and their GCF is 6, and one of the numbers is 30, what is the other number?

If the LCM of two numbers is equal to one of the numbers, what can you say about the relationship between the two numbers?

Prove that for any two positive integers a and b, GCF(a, b) × LCM(a, b) = a × b.

What is the least common multiple (LCM) of 18 and 24?