Question

teacher :
date :
find the least common multiple for each num
1 ) 20 , 24
2 ) 8 , 40
3 ) 6 , 40
4 ) 5 , 40
5 ) 3 , 20
6 ) 10 , 60
7 ) 6 , 10
8 ) 5 , 2
9 ) 20 , 3
10 ) 6 , 20
11 ) 6 , 4
12 ) 60 , 3
13 ) 12 , 5
14 ) 4 , 3
5 ) 3 , 5
) 60 , 6
) 10 , 40
40 20

Explanation:

Step1: Prime Factorization of 20 and 24

Prime factorize \(20 = 2^2\times5\) and \(24 = 2^3\times3\).

Step2: Find LCM by Taking Max Exponents

For each prime factor, take the highest power: \(2^3\), \(3^1\), \(5^1\). Then \(LCM = 2^3\times3\times5 = 8\times3\times5 = 120\).

Step3: Prime Factorization of 8 and 40

Prime factorize \(8 = 2^3\) and \(40 = 2^3\times5\).

Step4: Find LCM (Max Exponents)

Highest powers: \(2^3\), \(5^1\). So \(LCM = 2^3\times5 = 8\times5 = 40\).

Step5: Prime Factorization of 6 and 40

Prime factorize \(6 = 2\times3\) and \(40 = 2^3\times5\).

Step6: Find LCM (Max Exponents)

Highest powers: \(2^3\), \(3^1\), \(5^1\). \(LCM = 2^3\times3\times5 = 8\times3\times5 = 120\).

Step7: Prime Factorization of 5 and 40

Prime factorize \(5 = 5\) and \(40 = 2^3\times5\).

Step8: Find LCM (Max Exponents)

Highest powers: \(2^3\), \(5^1\). \(LCM = 2^3\times5 = 40\).

Step9: Prime Factorization of 3 and 20

Prime factorize \(3 = 3\) and \(20 = 2^2\times5\).

Step10: Find LCM (Max Exponents)

Highest powers: \(2^2\), \(3^1\), \(5^1\). \(LCM = 2^2\times3\times5 = 4\times3\times5 = 60\).

Step11: Prime Factorization of 10 and 60

Prime factorize \(10 = 2\times5\) and \(60 = 2^2\times3\times5\).

Step12: Find LCM (Max Exponents)

Highest powers: \(2^2\), \(3^1\), \(5^1\). \(LCM = 2^2\times3\times5 = 60\).

Step13: Prime Factorization of 6 and 10

Prime factorize \(6 = 2\times3\) and \(10 = 2\times5\).

Step14: Find LCM (Max Exponents)

Highest powers: \(2^1\), \(3^1\), \(5^1\). \(LCM = 2\times3\times5 = 30\).

Step15: Prime Factorization of 5 and 2

Prime factorize \(5 = 5\) and \(2 = 2\).

Step16: Find LCM (Max Exponents)

Highest powers: \(2^1\), \(5^1\). \(LCM = 2\times5 = 10\).

Step17: Prime Factorization of 20 and 3

Prime factorize \(20 = 2^2\times5\) and \(3 = 3\).

Step18: Find LCM (Max Exponents)

Highest powers: \(2^2\), \(3^1\), \(5^1\). \(LCM = 2^2\times3\times5 = 60\).

Step19: Prime Factorization of 6 and 20

Prime factorize \(6 = 2\times3\) and \(20 = 2^2\times5\).

Step20: Find LCM (Max Exponents)

Highest powers: \(2^2\), \(3^1\), \(5^1\). \(LCM = 2^2\times3\times5 = 60\).

Step21: Prime Factorization of 6 and 4

Prime factorize \(6 = 2\times3\) and \(4 = 2^2\).

Step22: Find LCM (Max Exponents)

Highest powers: \(2^2\), \(3^1\). \(LCM = 2^2\times3 = 12\).

Step23: Prime Factorization of 60 and 3

Prime factorize \(60 = 2^2\times3\times5\) and \(3 = 3\).

Step24: Find LCM (Max Exponents)

Highest powers: \(2^2\), \(3^1\), \(5^1\). \(LCM = 60\) (since 60 already has 3 as a factor).

Step25: Prime Factorization of 12 and 5

Prime factorize \(12 = 2^2\times3\) and \(5 = 5\).

Step26: Find LCM (Max Exponents)

Highest powers: \(2^2\), \(3^1\), \(5^1\). \(LCM = 2^2\times3\times5 = 60\).

Step27: Prime Factorization of 4 and 3

Prime factorize \(4 = 2^2\) and \(3 = 3\).

Step28: Find LCM (Max Exponents)

Highest powers: \(2^2\), \(3^1\). \(LCM = 2^2\times3 = 12\).

Step29: Prime Factorization of 3 and 5

Prime factorize \(3 = 3\) and \(5 = 5\).

Step30: Find LCM (Max Exponents)

Highest powers: \(3^1\), \(5^1\). \(LCM = 3\times5 = 15\).

Step31: Prime Factorization of 60 and 6

Prime factorize \(60 = 2^2\times3\times5\) and \(6 = 2\times3\).

Step32: Find LCM (Max Exponents)

Highest powers: \(2^2\), \(3^1\), \(5^1\). \(LCM = 60\) (60 has all factors of 6).

Step33: Prime Factorization of 10 and 40

Prime factorize \(10 = 2\times5\) and \(40 = 2^3\times5\).

Step34: Find LCM (Max Exponents)

Highest powers: \(2^3\), \(5^1\). \(LCM = 40\) (40 has all factors of 10).

Answer:

s (for each problem):

1. 120
2. 40
3. 120
4. 40
5. 60
6. 60
7. 30
8. 10
9. 60
10. 60
11. 12
12. 60
13. 60
14. 12
15. 15
16. 60
17. 40