Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 6 and 28 the smallest integer that is 84 that is divisible by both numbers.
Least Common Multiple (LCM) of 6 and 28 is 84.
LCM(6,28) = 84
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 6 and 28. First we will calculate the prime factors of 6 and 28.
Prime Factorization of 6
2 | 6 |
3 | 3 |
1 |
Prime factors of 6 are 2,3. Prime factorization of 6 in exponential form is:
6 = 21×31
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 6 and 28.
LCM(6,28) = 22×31×71
LCM(6,28) = 84
Factors of 6
List of positive integer factors of 6 that divides 6 without a remainder.
1, 2, 3, 6
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 6 and 28, than apply into the LCM equation.
GCF(6,28) = 2
LCM(6,28) = ( 6 × 28) / 2
LCM(6,28) = 168 / 2
LCM(6,28) = 84
(i) The LCM of 28 and 6 is associative
LCM of 6 and 28 = LCM of 28 and 6
1. What is the LCM of 6 and 28?
Answer: LCM of 6 and 28 is 84.
2. What are the Factors of 6?
Answer: Factors of 6 are 1, 2, 3, 6. There are 4 integers that are factors of 6. The greatest factor of 6 is 6.
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 6 and 28?
Answer:
Least Common Multiple of 6 and 28 = 84
Step 1: Find the prime factorization of 6
6 = 2 x 3
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 = 84 = 2 x 2 x 3 x 7
Step 4: Therefore, the least common multiple of 6 and 28 is 84.