Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 184 and 186 the smallest integer that is 17112 that is divisible by both numbers.
Least Common Multiple (LCM) of 184 and 186 is 17112.
LCM(184,186) = 17112
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 184 and 186. First we will calculate the prime factors of 184 and 186.
Prime Factorization of 184
2 | 184 |
2 | 92 |
2 | 46 |
23 | 23 |
1 |
Prime factors of 184 are 2,23. Prime factorization of 184 in exponential form is:
184 = 23×231
Prime Factorization of 186
2 | 186 |
3 | 93 |
31 | 31 |
1 |
Prime factors of 186 are 2, 3,31. Prime factorization of 186 in exponential form is:
186 = 21×31×311
Now multiplying the highest exponent prime factors to calculate the LCM of 184 and 186.
LCM(184,186) = 23×31×231×311
LCM(184,186) = 17112
Factors of 184
List of positive integer factors of 184 that divides 184 without a remainder.
1, 2, 4, 8, 23, 46, 92, 184
Factors of 186
List of positive integer factors of 186 that divides 186 without a remainder.
1, 2, 3, 6, 31, 62, 93, 186
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 184 and 186, than apply into the LCM equation.
GCF(184,186) = 2
LCM(184,186) = ( 184 × 186) / 2
LCM(184,186) = 34224 / 2
LCM(184,186) = 17112
(i) The LCM of 186 and 184 is associative
LCM of 184 and 186 = LCM of 186 and 184
1. What is the LCM of 184 and 186?
Answer: LCM of 184 and 186 is 17112.
2. What are the Factors of 184?
Answer: Factors of 184 are 1, 2, 4, 8, 23, 46, 92, 184. There are 8 integers that are factors of 184. The greatest factor of 184 is 184.
3. What are the Factors of 186?
Answer: Factors of 186 are 1, 2, 3, 6, 31, 62, 93, 186. There are 8 integers that are factors of 186. The greatest factor of 186 is 186.
4. How to Find the LCM of 184 and 186?
Answer:
Least Common Multiple of 184 and 186 = 17112
Step 1: Find the prime factorization of 184
184 = 2 x 2 x 2 x 23
Step 2: Find the prime factorization of 186
186 = 2 x 3 x 31
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 17112 = 2 x 2 x 2 x 3 x 23 x 31
Step 4: Therefore, the least common multiple of 184 and 186 is 17112.