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 28 the smallest integer that is 56 that is divisible by both numbers.
Least Common Multiple (LCM) of 8 and 28 is 56.
LCM(8,28) = 56
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 28. First we will calculate the prime factors of 8 and 28.
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 28
2 | 28 |
2 | 14 |
7 | 7 |
1 |
Prime factors of 28 are 2,7. Prime factorization of 28 in exponential form is:
28 = 22×71
Now multiplying the highest exponent prime factors to calculate the LCM of 8 and 28.
LCM(8,28) = 23×71
LCM(8,28) = 56
Factors of 8
List of positive integer factors of 8 that divides 8 without a remainder.
1, 2, 4, 8
Factors of 28
List of positive integer factors of 28 that divides 28 without a remainder.
1, 2, 4, 7, 14, 28
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8 and 28, than apply into the LCM equation.
GCF(8,28) = 4
LCM(8,28) = ( 8 × 28) / 4
LCM(8,28) = 224 / 4
LCM(8,28) = 56
(i) The LCM of 28 and 8 is associative
LCM of 8 and 28 = LCM of 28 and 8
1. What is the LCM of 8 and 28?
Answer: LCM of 8 and 28 is 56.
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 28?
Answer: Factors of 28 are 1, 2, 4, 7, 14, 28. There are 6 integers that are factors of 28. The greatest factor of 28 is 28.
4. How to Find the LCM of 8 and 28?
Answer:
Least Common Multiple of 8 and 28 = 56
Step 1: Find the prime factorization of 8
8 = 2 x 2 x 2
Step 2: Find the prime factorization of 28
28 = 2 x 2 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 56 = 2 x 2 x 2 x 7
Step 4: Therefore, the least common multiple of 8 and 28 is 56.