Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8 and 24 the smallest integer that is 24 that is divisible by both numbers.
Least Common Multiple (LCM) of 8 and 24 is 24.
LCM(8,24) = 24
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 8 and 24. First we will calculate the prime factors of 8 and 24.
Prime Factorization of 8
2 | 8 |
2 | 4 |
2 | 2 |
1 |
Prime factors of 8 are 2. Prime factorization of 8 in exponential form is:
8 = 23
Prime Factorization of 24
2 | 24 |
2 | 12 |
2 | 6 |
3 | 3 |
1 |
Prime factors of 24 are 2,3. Prime factorization of 24 in exponential form is:
24 = 23×31
Now multiplying the highest exponent prime factors to calculate the LCM of 8 and 24.
LCM(8,24) = 23×31
LCM(8,24) = 24
Factors of 8
List of positive integer factors of 8 that divides 8 without a remainder.
1, 2, 4, 8
Factors of 24
List of positive integer factors of 24 that divides 24 without a remainder.
1, 2, 3, 4, 6, 8, 12, 24
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8 and 24, than apply into the LCM equation.
GCF(8,24) = 8
LCM(8,24) = ( 8 × 24) / 8
LCM(8,24) = 192 / 8
LCM(8,24) = 24
(i) The LCM of 24 and 8 is associative
LCM of 8 and 24 = LCM of 24 and 8
1. What is the LCM of 8 and 24?
Answer: LCM of 8 and 24 is 24.
2. What are the Factors of 8?
Answer: Factors of 8 are 1, 2, 4, 8. There are 4 integers that are factors of 8. The greatest factor of 8 is 8.
3. What are the Factors of 24?
Answer: Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. There are 8 integers that are factors of 24. The greatest factor of 24 is 24.
4. How to Find the LCM of 8 and 24?
Answer:
Least Common Multiple of 8 and 24 = 24
Step 1: Find the prime factorization of 8
8 = 2 x 2 x 2
Step 2: Find the prime factorization of 24
24 = 2 x 2 x 2 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 24 = 2 x 2 x 2 x 3
Step 4: Therefore, the least common multiple of 8 and 24 is 24.