Download 1-4 Multiples: LCM and LCD

1-4 Multiples: LCM and LCD
Name
Date
Find the least common multiple (LCM)
of 21, 25, and 35.
• Find the prime factorization of each number.
21 3 • 7
25 5 • 5 35 5 • 7
52
• Write each prime factor the greatest number
of times it occurs in any of the numbers.
Multiply these factors to find the LCM.
3 • 7 • 52 525
So LCM 525.
Remember:
• If two numbers are relatively prime, the LCM
is the product of the numbers.
• If one number is a multiple of the other number,
the LCM is the greater number.
The least common denominator (LCD) of two or
more fractions is the LCM of their denominators.
2 16
Rename 5 27
, 9 , and 73 using the LCD.
2
2
5 27
5 • 27
137
27
27
16
9
•3
16
9•3
48
27
73 73 •• 99 63
27
Think
27 is a multiple
of 9 and 3.
LCM: 27
LCD: 27
2 16
48
63
So 5 27
, 9 , 73 137
27 , 27 , 27 .
Find the least common multiple (LCM).
1. 12 and 15
12 22 • 3
15 3 • 5
LCM 22 • 3 • 5 60
5. 12, 30, and 42
Copyright © by William H. Sadlier, Inc. All rights reserved.
420
2. 9 and 26
3. 10 and 16
234
6. 30, 45, and 150
80
7. 50, 75, and 125
450
750
4. 18, 30, and 60
180
8. 54, 63, and 108
756
For each pair of numbers, write the term that best applies: relatively prime
or multiple. Then find the LCM.
9. 15 and 45
multiple; 45
10. 8 and 9
11. 6 and 54
relatively prime; 72
multiple; 54
12. 11 and 20
relatively prime; 220
Find the LCM.
13. 45xyz and 75x5y2
45xyz •5•x•y•z
75x5y2 3 • 52 • x5 • y2
32 • 52 • x5 • y2 • z
225x5y2z
14. c2 and b2c3
15. 7x2y and 14xy2
16. 3r3 and 9r2t
32
17. 15a2bc and 30a2b2
30a2b2c
b2 c3
18. 6x2y and 4x3
14x2y2
9r3t
19. 3m2n and 15m2n2
20. 120a4b and 84a3b2
15m2n2
840a4b2
12x3y
Lesson 1-4, pages 8–9.
Chapter 1
7
For More Practice Go To:
Find the least common denominator (LCD).
2
and 49
21. 15
15 3 • 5
9 32
LCD 32 • 5 45
25
22. 144
and 29
54
432
4g
24e
23. 25e2f 3 and 125fg3
125e2f 3g3
12m
7m
24. 35n4p and 12n2p2
420n4p2
Rename the set of fractions using the LCD.
30 2 • 3 • 5; 8 23
23 • 3 • 5 120
7 4 28
30 4 120
3 15 45
120
8 15
4
29. 2 35 , 94 , 25
260 225
16
,
,
100 100
100
8
26. 56 and 15
16
25
,
30
30
30. 53 , 3 29 , 56
58
15
30
, ,
18 18
18
7
27. 13 , 56 , 12
4 10
7
12
, ,
12
12
2c
1
31. 3a2 , 12a2 , 6a
7
8c
2a
7
,
,
12a2
12a2 12a2
1
3
5
28. 12
, 16
, 18
12
27
40
,
,
144
144
144
9
8
32. 35b
, 11
50 , 7b
90
77b 400
,
,
350b
350b 350b
33. Lynne is making pins for a charity fundraiser.
She uses 1 pink bead and 1 white bead for
each pin. The pink beads come in bags of 48.
The white beads come in bags of 30. What is
the fewest number of bags of each color she
must buy to have the same number of white
beads and pink beads? How many pins will
she be able to make?
34. A landscaper is buying thyme, sage, and
lavender to plant along a walkway. Thyme
comes in flats of 36, lavender comes in flats
of 12, and sage comes in flats of 24. She
wants to have the same number of each type
of plant. What is the least number of flats
of each type she should buy? How many
plants of each type will she have?
48 • 3; 30 2 • 3 • 5; LCM of 48 and 30:
24 • 3 • 5 240; 240 48 5; 240 30 8
She must buy 5 bags of pink and
8 bags of white to make 240 pins.
36 22 • 32; 12 22 • 3; 24 23 • 3
LCM of 36, 12, and 24: 23 • 32 72
72 36 2; 72 12 6; 72 24 3
She should buy 2 thyme, 6 lavender,
and 3 sage to have 72 plants.
24
35. A pair of numbers has a GCF of 14 and LCM
of 168. What could the numbers be? Explain.
Answers may vary. GCF: 14 2 • 7 and
LCM: 168 23 • 3 • 7; both numbers must
have 2 and 7 as factors. So possible pair
of numbers would be 42 and 56.
8
Chapter 1
36. Twin primes are pairs of prime numbers, like
3 and 5, that differ by two. List the other pairs
of twin primes between 1 and 100.
5 and 7, 11 and 13, 17 and 19, 29 and 31,
41 and 43, 59 and 61, 71 and 73
Copyright © by William H. Sadlier, Inc. All rights reserved.
7
and 38
25. 30