Warm up

1

• Warm up
• Beginning with the number itself write the
• first five multiples of each number.
• 6
• 8
• Write the prime factorization of each
• number.
• 3. 44
• 4. 350

2

• 6 6, 12, 18, 24, 30
• 8 8. 16. 24. 32. 40
• 44- 2² x 11
• 35 0 - 2 x 5² x 7

3
Least common Multiples (LCM) When two numbers
have some multiples that are the same these
multiples are called common multiples. The least
common multiple (LCM) is the smallest non-zero
common multiple. You can make a list of the
common multiples to find the LCM.
4
Paul will water his yard every 3 days and mow the
lawn every 7 days. When is the first day he will
do both? Find the least common multiple of 3 and
7. 3, 6, 9, 12, 15 ,18, 21, 24, 27, 30, 33, 36,
39, 42, 45. 7, 14,21, 35, 42, 49, 56, 63, 70,
77, 84, 91, 98, 105.. 21. 42 The first day he
will do both is the 21st. Making a list to find
the LCM for larger numbers can be impractical.
5
LCM can also be found using prime factorization.
The LCM is found by multiplying the highest power
of each prime factor. Use prime factorization to
find the LCM of 30 and 45. 30 5 x 2 x 3 45
5 x 3 x 3 3² x 5 Identify the highest power
of each prime factor 2, 3², and 5 2 x 3² x 5 2
x 9 x 5 90 The LCM of 30 and 45 is 90.
6

• Find the LCM for each pair of numbers,
• 16, 12
• 34, 18
• 15x, 45y
• 8k, 20k, 24k²

7
Find the LCM for each pair of numbers, 1. 16, 12
48 2. 34, 18 306
3. 15x, 45y 45xy 4. 8k, 20k, 24k²
120k²
8

• Find the least common denominator (LCD) for each
  set of fractions.
• 1. ½, 1/3
• 2. ¼, 3/8
• 3/5, 3/10
• 1/7x, 1/9x
• 3/8m, 7/9k

9
1. ½, 1/3 6 2. ¼, 3/8
8 3. 3/5, 3/10 10 4. 1/7x, 1/9x 63x 5.
3/8m, 7/9k 72mk
10
Write lt or gt between each fraction to make a true
statement. 1. 2/3 5/9 2. 1/3
5/6 3. 1/5 3/7 4. 5/9 7/12
11
Write lt or gt between each fraction to make a true
statement. 1. 2/3 gt 5/9 2. 1/3 lt
5/6 3. 1/5 lt 3/7 4. 5/9 lt 7/12