Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 232 and 237 the smallest integer that is 54984 that is divisible by both numbers.
Least Common Multiple (LCM) of 232 and 237 is 54984.
LCM(232,237) = 54984
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 232 and 237. First we will calculate the prime factors of 232 and 237.
Prime Factorization of 232
2 | 232 |
2 | 116 |
2 | 58 |
29 | 29 |
1 |
Prime factors of 232 are 2,29. Prime factorization of 232 in exponential form is:
232 = 23×291
Prime Factorization of 237
3 | 237 |
79 | 79 |
1 |
Prime factors of 237 are 3,79. Prime factorization of 237 in exponential form is:
237 = 31×791
Now multiplying the highest exponent prime factors to calculate the LCM of 232 and 237.
LCM(232,237) = 23×31×291×791
LCM(232,237) = 54984
Factors of 232
List of positive integer factors of 232 that divides 232 without a remainder.
1, 2, 4, 8, 29, 58, 116, 232
Factors of 237
List of positive integer factors of 237 that divides 237 without a remainder.
1, 3, 79, 237
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 232 and 237, than apply into the LCM equation.
GCF(232,237) = 1
LCM(232,237) = ( 232 × 237) / 1
LCM(232,237) = 54984 / 1
LCM(232,237) = 54984
(i) The LCM of 237 and 232 is associative
LCM of 232 and 237 = LCM of 237 and 232
1. What is the LCM of 232 and 237?
Answer: LCM of 232 and 237 is 54984.
2. What are the Factors of 232?
Answer: Factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232. There are 8 integers that are factors of 232. The greatest factor of 232 is 232.
3. What are the Factors of 237?
Answer: Factors of 237 are 1, 3, 79, 237. There are 4 integers that are factors of 237. The greatest factor of 237 is 237.
4. How to Find the LCM of 232 and 237?
Answer:
Least Common Multiple of 232 and 237 = 54984
Step 1: Find the prime factorization of 232
232 = 2 x 2 x 2 x 29
Step 2: Find the prime factorization of 237
237 = 3 x 79
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 54984 = 2 x 2 x 2 x 3 x 29 x 79
Step 4: Therefore, the least common multiple of 232 and 237 is 54984.