Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 111 and 114 the smallest integer that is 4218 that is divisible by both numbers.
Least Common Multiple (LCM) of 111 and 114 is 4218.
LCM(111,114) = 4218
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 111 and 114. First we will calculate the prime factors of 111 and 114.
Prime Factorization of 111
3 | 111 |
37 | 37 |
1 |
Prime factors of 111 are 3,37. Prime factorization of 111 in exponential form is:
111 = 31×371
Prime Factorization of 114
2 | 114 |
3 | 57 |
19 | 19 |
1 |
Prime factors of 114 are 2, 3,19. Prime factorization of 114 in exponential form is:
114 = 21×31×191
Now multiplying the highest exponent prime factors to calculate the LCM of 111 and 114.
LCM(111,114) = 21×31×191×371
LCM(111,114) = 4218
Factors of 111
List of positive integer factors of 111 that divides 111 without a remainder.
1, 3, 37, 111
Factors of 114
List of positive integer factors of 114 that divides 114 without a remainder.
1, 2, 3, 6, 19, 38, 57, 114
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 111 and 114, than apply into the LCM equation.
GCF(111,114) = 3
LCM(111,114) = ( 111 × 114) / 3
LCM(111,114) = 12654 / 3
LCM(111,114) = 4218
(i) The LCM of 114 and 111 is associative
LCM of 111 and 114 = LCM of 114 and 111
1. What is the LCM of 111 and 114?
Answer: LCM of 111 and 114 is 4218.
2. What are the Factors of 111?
Answer: Factors of 111 are 1, 3, 37, 111. There are 4 integers that are factors of 111. The greatest factor of 111 is 111.
3. What are the Factors of 114?
Answer: Factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114. There are 8 integers that are factors of 114. The greatest factor of 114 is 114.
4. How to Find the LCM of 111 and 114?
Answer:
Least Common Multiple of 111 and 114 = 4218
Step 1: Find the prime factorization of 111
111 = 3 x 37
Step 2: Find the prime factorization of 114
114 = 2 x 3 x 19
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4218 = 2 x 3 x 19 x 37
Step 4: Therefore, the least common multiple of 111 and 114 is 4218.