Lesson 7: Find Factors and Multiples6.NOS.4

I can…

I can find the greatest common factor and the least common multiple of two numbers, and use each to solve a real problem.

Key words

• Find Factors and Multiples — List the factors and multiples, then see what two numbers share.
• Factor — A number that goes into a number with none left.
• Multiple — A number you land on when you count by it.
• Greatest common factor (GCF) — The biggest number that goes into both.
• Least common multiple (LCM) — The smallest number both numbers count up to.
• Factor pair — Two numbers that give the number as a product.
• Prime factorization — A number written as a product of primes.
• Common factor — A number that divides two numbers with none left over.
• Greatest common factor — The biggest number that goes into both.
• Least common multiple — The smallest number both numbers count up to.

Steps

1. The store has 48 pencils and 36 notebooks. Every combo pack must hold the same number of each, with nothing left over — so the number of packs has to be a factor of BOTH quantities.
2. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Listing them in order is what makes the comparison easy.
3. The numbers in both lists are the common factors: 1, 2, 3, 4, 6, and 12.
4. The greatest of those is 12, so the GCF of 48 and 36 is 12. The manager can make 12 combo packs — each holding 48 ÷ 12 = 4 pencils and 36 ÷ 12 = 3 notebooks.

Try it

At home, the dog gets a bath every 4 weeks and the cat gets its medicine every 6 weeks, and both happen this week. When will they next happen in the same week?

Check your answer

Week 12, the least common multiple of 4 and 6

Repeating cycles land on multiples. Multiples of 4 are 4, 8, 12 … and of 6 are 6, 12 …, so the first shared week is 12 — the LCM.

Sentence starter

I know ___ because ___.

Goal: I can explain my choice using the words factor, multiple, common, greatest, and least.