4. 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?

Question

4. 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

## Step 1: Finding the Least Common Multiple (LCM)### We need to find the smallest number that is divisible by 6, 4, and 10. This is the least common multiple (LCM) of 6, 4, and 10. We can find the LCM by prime factorization.## Step 2: Prime Factorization###

###

## Step 3: Calculating the LCM### The LCM is the product of the highest powers of all prime factors present in the numbers. So, LCM

.## Step 4: Considering the Starting and Ending Red Beads### Since each strand starts and ends with a red bead, and red beads occur every 60th bead, the minimum number of beads each strand can have is 60.

Question

4. 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?

Solution

Answer

Explanation