I need help with this LCM word problem

Question

A necklace has 3 strands of beads. Each strand begins and ends with a red bead. If a red bead occurs every 6th bead on one strand, every 4th bead on the second strand, and every 10th bead on the third strand, what is the least number of beads each strand can have?

Answer 1

To find the least common multiple of a set of numbers:

 

1) factor each number in primes; 6 = 2 · 3, 4 = 2 · 2, 10 = 2 · 5 

2) the LCM must contain at least one of each different factor: 2, 3, 5

3) the LCM must contain each factor the most it appears in any one factorization. The only one have more than one appearance is the 2.

 

The LCM = 2² · 3 · 5

The LCM = 60.

Answer 2

Hi Sara--

 

The answer will be the Least Common Multiple of all three numbers; that is, the smallest multiple they all have.

 

Start counting up by 4's from 4 until you get to a multiple of 10. Then do the same by 6's from 6, and then by 10's from 10.

 

Repeat the process until you have a number that appears on all 3 lists, and that's your LCM, and the minimum number of beads.

 

Hope this helps!

 

Matt in New York