Multiples: LCM and LCD

Honors Math – Grade 7

Problem of the DayA botanist waters a plant every 4th day and gives it plant food every 6th day. If the botanist gives both water and plant food on April 1, what is the next date in April when the plant will receive both?

To find the next date, find the least common multiple (LCM) of 4 and 6.

The Least Common Multiple (LCM) is the least nonzero multiple that is common to all of the numbers. A multiple of a number is the product of that number and any whole number.

VOCABULARY ALERT

The Prime Factorization of a number can be used to find the LCM of two or more numbers.

To use the prime factorization to find the LCM:1. Make a factor tree for each number.2. Write each prime factor the greatest number of times it

occurs in any of the numbers. 3. Multiply these factors..

Using Factor Trees to find the LCM.

The plant will receive both water and plant food 12 days later, on April 13.

Remember, the LCD of two or more fractions is the LCM of the denominators!

Find the LCM.

17535 and

2415 and

246 and

The LCD is used to rename fractions with unlike denominators.

5

4,

4

3,

3

2

8

31,

4

17,

16

73

Find the LCD and rename the set of fractions using the LCD.

5

1,

7

3,

6

5

18

5,

16

32,

12

1

4

11,

12

53,

6

7