Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 166 and 167 the smallest integer that is 27722 that is divisible by both numbers.
Least Common Multiple (LCM) of 166 and 167 is 27722.
LCM(166,167) = 27722
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 166 and 167. First we will calculate the prime factors of 166 and 167.
Prime Factorization of 166
2 | 166 |
83 | 83 |
1 |
Prime factors of 166 are 2,83. Prime factorization of 166 in exponential form is:
166 = 21×831
Prime Factorization of 167
167 | 167 |
1 |
Prime factors of 167 are 167. Prime factorization of 167 in exponential form is:
167 = 1671
Now multiplying the highest exponent prime factors to calculate the LCM of 166 and 167.
LCM(166,167) = 21×831×1671
LCM(166,167) = 27722
Factors of 166
List of positive integer factors of 166 that divides 166 without a remainder.
1, 2, 83, 166
Factors of 167
List of positive integer factors of 167 that divides 167 without a remainder.
1, 167
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 166 and 167, than apply into the LCM equation.
GCF(166,167) = 1
LCM(166,167) = ( 166 × 167) / 1
LCM(166,167) = 27722 / 1
LCM(166,167) = 27722
(i) The LCM of 167 and 166 is associative
LCM of 166 and 167 = LCM of 167 and 166
1. What is the LCM of 166 and 167?
Answer: LCM of 166 and 167 is 27722.
2. What are the Factors of 166?
Answer: Factors of 166 are 1, 2, 83, 166. There are 4 integers that are factors of 166. The greatest factor of 166 is 166.
3. What are the Factors of 167?
Answer: Factors of 167 are 1, 167. There are 2 integers that are factors of 167. The greatest factor of 167 is 167.
4. How to Find the LCM of 166 and 167?
Answer:
Least Common Multiple of 166 and 167 = 27722
Step 1: Find the prime factorization of 166
166 = 2 x 83
Step 2: Find the prime factorization of 167
167 = 167
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 27722 = 2 x 83 x 167
Step 4: Therefore, the least common multiple of 166 and 167 is 27722.