Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 242 and 249 the smallest integer that is 60258 that is divisible by both numbers.
Least Common Multiple (LCM) of 242 and 249 is 60258.
LCM(242,249) = 60258
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 242 and 249. First we will calculate the prime factors of 242 and 249.
Prime Factorization of 242
2 | 242 |
11 | 121 |
11 | 11 |
1 |
Prime factors of 242 are 2,11. Prime factorization of 242 in exponential form is:
242 = 21×112
Prime Factorization of 249
3 | 249 |
83 | 83 |
1 |
Prime factors of 249 are 3,83. Prime factorization of 249 in exponential form is:
249 = 31×831
Now multiplying the highest exponent prime factors to calculate the LCM of 242 and 249.
LCM(242,249) = 21×31×112×831
LCM(242,249) = 60258
Factors of 242
List of positive integer factors of 242 that divides 242 without a remainder.
1, 2, 11, 22, 121, 242
Factors of 249
List of positive integer factors of 249 that divides 249 without a remainder.
1, 3, 83, 249
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 242 and 249, than apply into the LCM equation.
GCF(242,249) = 1
LCM(242,249) = ( 242 × 249) / 1
LCM(242,249) = 60258 / 1
LCM(242,249) = 60258
(i) The LCM of 249 and 242 is associative
LCM of 242 and 249 = LCM of 249 and 242
1. What is the LCM of 242 and 249?
Answer: LCM of 242 and 249 is 60258.
2. What are the Factors of 242?
Answer: Factors of 242 are 1, 2, 11, 22, 121, 242. There are 6 integers that are factors of 242. The greatest factor of 242 is 242.
3. What are the Factors of 249?
Answer: Factors of 249 are 1, 3, 83, 249. There are 4 integers that are factors of 249. The greatest factor of 249 is 249.
4. How to Find the LCM of 242 and 249?
Answer:
Least Common Multiple of 242 and 249 = 60258
Step 1: Find the prime factorization of 242
242 = 2 x 11 x 11
Step 2: Find the prime factorization of 249
249 = 3 x 83
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 60258 = 2 x 3 x 11 x 11 x 83
Step 4: Therefore, the least common multiple of 242 and 249 is 60258.