Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 162 and 165 the smallest integer that is 8910 that is divisible by both numbers.
Least Common Multiple (LCM) of 162 and 165 is 8910.
LCM(162,165) = 8910
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 162 and 165. First we will calculate the prime factors of 162 and 165.
Prime Factorization of 162
2 | 162 |
3 | 81 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
Prime factors of 162 are 2,3. Prime factorization of 162 in exponential form is:
162 = 21×34
Prime Factorization of 165
3 | 165 |
5 | 55 |
11 | 11 |
1 |
Prime factors of 165 are 3, 5,11. Prime factorization of 165 in exponential form is:
165 = 31×51×111
Now multiplying the highest exponent prime factors to calculate the LCM of 162 and 165.
LCM(162,165) = 21×34×51×111
LCM(162,165) = 8910
Factors of 162
List of positive integer factors of 162 that divides 162 without a remainder.
1, 2, 3, 6, 9, 18, 27, 54, 81, 162
Factors of 165
List of positive integer factors of 165 that divides 165 without a remainder.
1, 3, 5, 11, 15, 33, 55, 165
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 162 and 165, than apply into the LCM equation.
GCF(162,165) = 3
LCM(162,165) = ( 162 × 165) / 3
LCM(162,165) = 26730 / 3
LCM(162,165) = 8910
(i) The LCM of 165 and 162 is associative
LCM of 162 and 165 = LCM of 165 and 162
1. What is the LCM of 162 and 165?
Answer: LCM of 162 and 165 is 8910.
2. What are the Factors of 162?
Answer: Factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162. There are 10 integers that are factors of 162. The greatest factor of 162 is 162.
3. What are the Factors of 165?
Answer: Factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165. There are 8 integers that are factors of 165. The greatest factor of 165 is 165.
4. How to Find the LCM of 162 and 165?
Answer:
Least Common Multiple of 162 and 165 = 8910
Step 1: Find the prime factorization of 162
162 = 2 x 3 x 3 x 3 x 3
Step 2: Find the prime factorization of 165
165 = 3 x 5 x 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 8910 = 2 x 3 x 3 x 3 x 3 x 5 x 11
Step 4: Therefore, the least common multiple of 162 and 165 is 8910.