Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 42 and 52 the smallest integer that is 1092 that is divisible by both numbers.
Least Common Multiple (LCM) of 42 and 52 is 1092.
LCM(42,52) = 1092
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 42 and 52. First we will calculate the prime factors of 42 and 52.
Prime Factorization of 42
2 | 42 |
3 | 21 |
7 | 7 |
1 |
Prime factors of 42 are 2, 3,7. Prime factorization of 42 in exponential form is:
42 = 21×31×71
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
Now multiplying the highest exponent prime factors to calculate the LCM of 42 and 52.
LCM(42,52) = 22×31×71×131
LCM(42,52) = 1092
Factors of 42
List of positive integer factors of 42 that divides 42 without a remainder.
1, 2, 3, 6, 7, 14, 21, 42
Factors of 52
List of positive integer factors of 52 that divides 52 without a remainder.
1, 2, 4, 13, 26, 52
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42 and 52, than apply into the LCM equation.
GCF(42,52) = 2
LCM(42,52) = ( 42 × 52) / 2
LCM(42,52) = 2184 / 2
LCM(42,52) = 1092
(i) The LCM of 52 and 42 is associative
LCM of 42 and 52 = LCM of 52 and 42
1. What is the LCM of 42 and 52?
Answer: LCM of 42 and 52 is 1092.
2. What are the Factors of 42?
Answer: Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. There are 8 integers that are factors of 42. The greatest factor of 42 is 42.
3. 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.
4. How to Find the LCM of 42 and 52?
Answer:
Least Common Multiple of 42 and 52 = 1092
Step 1: Find the prime factorization of 42
42 = 2 x 3 x 7
Step 2: Find the prime factorization of 52
52 = 2 x 2 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1092 = 2 x 2 x 3 x 7 x 13
Step 4: Therefore, the least common multiple of 42 and 52 is 1092.