Equivalent Fractions And Lcm Worksheet With Answers (Page 3 of 7) in pdf

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Unit 4 – Number Patterns and Fractions

Lesson 3 – Equivalent Fractions and LCM

Solutions

1. The greatest common factor (GCF) of 8 and 20 is 4, and the least common multiple

(LCM) of 8 and 20 is 40. Their product is 4 x 40 = 160. Note that 8 x 20 = 160, also.

In general, the GCF( a , b ) x LCM( a , b ) = a x b .

2. There are four multiples of 89 between 600 and 900: 7 x 89 = 623, 8 x 89 = 712, 9 x

89 = 801, and 10 x 89 = 890. The sum of any three consecutive integers is always a

multiple of 3. Since 89 is prime and 9 is the only multiple of 3 in our list, the sum of

the three consecutive integers can only be 801. Incidentally, the three consecutive

integers are 266, 267 and 268.

3. There are 16 multiples of 3 less than 50 and 12 multiples of 4. We have counted the

4 multiples of 12 twice, however, so we must subtract 4. That’s 16 + 12 – 4 = 24 so

far. Now we need to exclude any multiples of five we might have counted. Those

would be the 3 multiples of 15 (15, 30 and 45) and the 2 multiples of 20 ( 20 and 40).

That leaves 24 – 3 - 2 = 19 integers less than 50 that are multiples of 3 or 4, but not

4. We know that we are numbering houses from 4 through 120, but using only the

multiples of four. We could list these out, but let’s see if we can count them quickly.

Since 4 = 4 x 1 and 120 = 4 x 30, we are working with the first 30 multiples of 4.

Unfortunately, some are one-digit integers, others are two-digit integers and still

others have three digits. Let’s group them accordingly. (It helps to know that 100 is

the first three-digit multiple of 4.)

1-digit

2-digit

3-digit

4x1 = 4

4x3 = 12

4x25 = 100

4x2 = 8

•

4x24 = 96

4x30 = 120

2 mult.

24 – 2 = 22 mult.

30 – 24 = 6 mult.

The two one-digit multiples account for a total of two digits; there are 22 two-digit

multiples, resulting in 22x2 = 44 digits; and there are six three-digit multiples

yielding 6x3 = 18 digits. This is a total of 2 + 44 + 18 = 64 digits, which will cost 64 x

$0.50 = $32.

5. Any common multiple will work, however, the LCM is smallest. This makes

multiplication easier.

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