Sure! Let's calculate the Least Common Multiple (LCM) of each set of numbers using prime factorization.
### a. LCM of 36 and 40
1. Prime factorization:
- 36 = 2² 3²
- 40 = 2³ 5
2. Taking the highest power of each prime:
- [tex]\(2^3, 3^2, 5^1\)[/tex]
3. Multiplying these together:
- [tex]\(LCM = 2^3 3^2 5 = 8 9 5 = 360\)[/tex]
### b. LCM of 15, 30, and 50
1. Prime factorization:
- 15 = 3 5
- 30 = 2 3 5
- 50 = 2 5²
2. Taking the highest power of each prime:
- [tex]\(2^1, 3^1, 5^2\)[/tex]
3. Multiplying these together:
- [tex]\(LCM = 2 3 5^2 = 2 3 25 = 150\)[/tex]
### c. LCM of 12, 30, and 90
1. Prime factorization:
- 12 = 2² 3
- 30 = 2 3 5
- 90 = 2 3² 5
2. Taking the highest power of each prime:
- [tex]\(2^2, 3^2, 5^1\)[/tex]
3. Multiplying these together:
- [tex]\(LCM = 2^2 3^2 5 = 4 9 5 = 180\)[/tex]
### d. LCM of 64, 80, and 100
1. Prime factorization:
- 64 = 2^6
- 80 = 2^4 5
- 100 = 2² 5²
2. Taking the highest power of each prime:
- [tex]\(2^6, 5^2\)[/tex]
3. Multiplying these together:
- [tex]\(LCM = 2^6 5^2 = 64 25 = 1600\)[/tex]
### e. LCM of 72, 90, and 120
1. Prime factorization:
- 72 = 2^3 3²
- 90 = 2 3² 5
- 120 = 2³ 3 5
2. Taking the highest power of each prime:
- [tex]\(2^3, 3^2, 5^1\)[/tex]
3. Multiplying these together:
- [tex]\(LCM = 2^3 3^2 5 = 8 9 5 = 360\)[/tex]
### f. LCM of 35, 40, and 95
1. Prime factorization:
- 35 = 5 7
- 40 = 2³ 5
- 95 = 5 19
2. Taking the highest power of each prime:
- [tex]\(2^3, 5^1, 7^1, 19^1\)[/tex]
3. Multiplying these together:
- [tex]\(LCM = 2^3 5 7 19 = 8 5 7 * 19 = 5320\)[/tex]
So, the LCM values are:
- a. 360
- b. 150
- c. 180
- d. 1600
- e. 360
- f. 5320
