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 117 the smallest integer that is 4329 that is divisible by both numbers.
Least Common Multiple (LCM) of 111 and 117 is 4329.
LCM(111,117) = 4329
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 117. First we will calculate the prime factors of 111 and 117.
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 117
3 | 117 |
3 | 39 |
13 | 13 |
1 |
Prime factors of 117 are 3,13. Prime factorization of 117 in exponential form is:
117 = 32×131
Now multiplying the highest exponent prime factors to calculate the LCM of 111 and 117.
LCM(111,117) = 32×131×371
LCM(111,117) = 4329
Factors of 111
List of positive integer factors of 111 that divides 111 without a remainder.
1, 3, 37, 111
Factors of 117
List of positive integer factors of 117 that divides 117 without a remainder.
1, 3, 9, 13, 39, 117
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 111 and 117, than apply into the LCM equation.
GCF(111,117) = 3
LCM(111,117) = ( 111 × 117) / 3
LCM(111,117) = 12987 / 3
LCM(111,117) = 4329
(i) The LCM of 117 and 111 is associative
LCM of 111 and 117 = LCM of 117 and 111
1. What is the LCM of 111 and 117?
Answer: LCM of 111 and 117 is 4329.
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 117?
Answer: Factors of 117 are 1, 3, 9, 13, 39, 117. There are 6 integers that are factors of 117. The greatest factor of 117 is 117.
4. How to Find the LCM of 111 and 117?
Answer:
Least Common Multiple of 111 and 117 = 4329
Step 1: Find the prime factorization of 111
111 = 3 x 37
Step 2: Find the prime factorization of 117
117 = 3 x 3 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4329 = 3 x 3 x 13 x 37
Step 4: Therefore, the least common multiple of 111 and 117 is 4329.