Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 52 and 67 the smallest integer that is 3484 that is divisible by both numbers.
Least Common Multiple (LCM) of 52 and 67 is 3484.
LCM(52,67) = 3484
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 52 and 67. First we will calculate the prime factors of 52 and 67.
Prime Factorization of 52
2 | 52 |
2 | 26 |
13 | 13 |
1 |
Prime factors of 52 are 2,13. Prime factorization of 52 in exponential form is:
52 = 22×131
Prime Factorization of 67
67 | 67 |
1 |
Prime factors of 67 are 67. Prime factorization of 67 in exponential form is:
67 = 671
Now multiplying the highest exponent prime factors to calculate the LCM of 52 and 67.
LCM(52,67) = 22×131×671
LCM(52,67) = 3484
Factors of 52
List of positive integer factors of 52 that divides 52 without a remainder.
1, 2, 4, 13, 26, 52
Factors of 67
List of positive integer factors of 67 that divides 67 without a remainder.
1, 67
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 52 and 67, than apply into the LCM equation.
GCF(52,67) = 1
LCM(52,67) = ( 52 × 67) / 1
LCM(52,67) = 3484 / 1
LCM(52,67) = 3484
(i) The LCM of 67 and 52 is associative
LCM of 52 and 67 = LCM of 67 and 52
1. What is the LCM of 52 and 67?
Answer: LCM of 52 and 67 is 3484.
2. What are the Factors of 52?
Answer: Factors of 52 are 1, 2, 4, 13, 26, 52. There are 6 integers that are factors of 52. The greatest factor of 52 is 52.
3. What are the Factors of 67?
Answer: Factors of 67 are 1, 67. There are 2 integers that are factors of 67. The greatest factor of 67 is 67.
4. How to Find the LCM of 52 and 67?
Answer:
Least Common Multiple of 52 and 67 = 3484
Step 1: Find the prime factorization of 52
52 = 2 x 2 x 13
Step 2: Find the prime factorization of 67
67 = 67
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3484 = 2 x 2 x 13 x 67
Step 4: Therefore, the least common multiple of 52 and 67 is 3484.