# Division/Multiplication

#### Cjnschool

##### New member
The 2-way radio Marcus wants runs on 6 batteries. The store sells batteries in packs of 10. What is the LEAST number of packs of batteries Marcus should so he has sets of batteries for the radio with no batteries left over?

#### Otis

##### Senior Member
Hello Cjnschool. When you first logged in, did you see the request to read the forum's guidelines? Please post what you've already tried or thought about, and we can go from there.

Here's a hint: The LCM of 6 and 10 (Least Common Multiple) has something to do with this exercise. Tell us what that LCM is, and we can explain why it helps. If you haven't learned about common multiples, let us know. • topsquark

#### Jomo

##### Elite Member
You really need to try to figure this out.
Suppose you buy 10 batteries:10-6=4---so you have 4 batteries left over,
Suppose you buy 20 batteries:20-6=14, 14-6 =8, 8-6 = 2---so you have 2 batteries left over.
Suppose you buy 30 batteries: 30 -6=24, 24- 6 = 18 -------can you finish from here?

I understand that your title is Division/Multiplication and I used subtraction. Please understand that I used repeated subtraction which is just division.

#### Cjnschool

##### New member
Hello Cjnschool. When you first logged in, did you see the request to read the forum's guidelines? Please post what you've already tried or thought about, and we can go from there.

Here's a hint: The LCM of 6 and 10 (Least Common Multiple) has something to do with this exercise. Tell us what that LCM is, and we can explain why it helps. If you haven't learned about common multiples, let us know. The LCM is 30

#### Subhotosh Khan

##### Super Moderator
Staff member
The LCM is 30
Now refer back to response #3 above - and complete the solution.

#### Otis

##### Senior Member
The LCM is 30

The number of batteries purchased must reflect two things: It must be a multiple of 10 (because Marcus may purchase batteries only in packs of 10), and it must be a multiple of 6 (because Marcus does not want any batteries left over, after grouping the purchased batteries into sets of six).

There are many numbers that are common multiples of 6 and 10, but the exercise asks for the smallest one (30).

So the answer is, "The least number of battery packs that Marcus should buy is 30".

Here is a visual. Each square below is a battery. Each row is a pack of ten batteries. Groups of six are shown in red.

1 Pack / 4 left over
■■■■■■ $$\quad$$ ■■■■

2 Packs / 2 left over
■■■■■■ $$\quad$$ ■■■■
■■■■■■ $$\quad$$ ■■
■■

3 Packs / 0 left over
■■■■■■ $$\quad$$ ■■■■
■■■■■■ $$\quad$$ ■■ $$\quad \; \quad$$ ■■
■■■■■■ $$\quad$$ $$\;$$ $$\;$$ $$\;$$ $$\quad$$ ■■■■

30 ÷ 6 = 5 sets of radio batteries

30 ÷ 10 = 3 battery packs • Subhotosh Khan and topsquark