Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 287 and 292 the smallest integer that is 83804 that is divisible by both numbers.
Least Common Multiple (LCM) of 287 and 292 is 83804.
LCM(287,292) = 83804
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 287 and 292. First we will calculate the prime factors of 287 and 292.
Prime Factorization of 287
7 | 287 |
41 | 41 |
1 |
Prime factors of 287 are 7,41. Prime factorization of 287 in exponential form is:
287 = 71×411
Prime Factorization of 292
2 | 292 |
2 | 146 |
73 | 73 |
1 |
Prime factors of 292 are 2,73. Prime factorization of 292 in exponential form is:
292 = 22×731
Now multiplying the highest exponent prime factors to calculate the LCM of 287 and 292.
LCM(287,292) = 22×71×411×731
LCM(287,292) = 83804
Factors of 287
List of positive integer factors of 287 that divides 287 without a remainder.
1, 7, 41, 287
Factors of 292
List of positive integer factors of 292 that divides 292 without a remainder.
1, 2, 4, 73, 146, 292
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 287 and 292, than apply into the LCM equation.
GCF(287,292) = 1
LCM(287,292) = ( 287 × 292) / 1
LCM(287,292) = 83804 / 1
LCM(287,292) = 83804
(i) The LCM of 292 and 287 is associative
LCM of 287 and 292 = LCM of 292 and 287
1. What is the LCM of 287 and 292?
Answer: LCM of 287 and 292 is 83804.
2. What are the Factors of 287?
Answer: Factors of 287 are 1, 7, 41, 287. There are 4 integers that are factors of 287. The greatest factor of 287 is 287.
3. What are the Factors of 292?
Answer: Factors of 292 are 1, 2, 4, 73, 146, 292. There are 6 integers that are factors of 292. The greatest factor of 292 is 292.
4. How to Find the LCM of 287 and 292?
Answer:
Least Common Multiple of 287 and 292 = 83804
Step 1: Find the prime factorization of 287
287 = 7 x 41
Step 2: Find the prime factorization of 292
292 = 2 x 2 x 73
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 83804 = 2 x 2 x 7 x 41 x 73
Step 4: Therefore, the least common multiple of 287 and 292 is 83804.