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 290 the smallest integer that is 83230 that is divisible by both numbers.
Least Common Multiple (LCM) of 287 and 290 is 83230.
LCM(287,290) = 83230
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 290. First we will calculate the prime factors of 287 and 290.
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 290
2 | 290 |
5 | 145 |
29 | 29 |
1 |
Prime factors of 290 are 2, 5,29. Prime factorization of 290 in exponential form is:
290 = 21×51×291
Now multiplying the highest exponent prime factors to calculate the LCM of 287 and 290.
LCM(287,290) = 21×51×71×291×411
LCM(287,290) = 83230
Factors of 287
List of positive integer factors of 287 that divides 287 without a remainder.
1, 7, 41, 287
Factors of 290
List of positive integer factors of 290 that divides 290 without a remainder.
1, 2, 5, 10, 29, 58, 145, 290
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 287 and 290, than apply into the LCM equation.
GCF(287,290) = 1
LCM(287,290) = ( 287 × 290) / 1
LCM(287,290) = 83230 / 1
LCM(287,290) = 83230
(i) The LCM of 290 and 287 is associative
LCM of 287 and 290 = LCM of 290 and 287
1. What is the LCM of 287 and 290?
Answer: LCM of 287 and 290 is 83230.
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 290?
Answer: Factors of 290 are 1, 2, 5, 10, 29, 58, 145, 290. There are 8 integers that are factors of 290. The greatest factor of 290 is 290.
4. How to Find the LCM of 287 and 290?
Answer:
Least Common Multiple of 287 and 290 = 83230
Step 1: Find the prime factorization of 287
287 = 7 x 41
Step 2: Find the prime factorization of 290
290 = 2 x 5 x 29
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 83230 = 2 x 5 x 7 x 29 x 41
Step 4: Therefore, the least common multiple of 287 and 290 is 83230.