Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 161 and 168 the smallest integer that is 3864 that is divisible by both numbers.
Least Common Multiple (LCM) of 161 and 168 is 3864.
LCM(161,168) = 3864
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 161 and 168. First we will calculate the prime factors of 161 and 168.
Prime Factorization of 161
7 | 161 |
23 | 23 |
1 |
Prime factors of 161 are 7,23. Prime factorization of 161 in exponential form is:
161 = 71×231
Prime Factorization of 168
2 | 168 |
2 | 84 |
2 | 42 |
3 | 21 |
7 | 7 |
1 |
Prime factors of 168 are 2, 3,7. Prime factorization of 168 in exponential form is:
168 = 23×31×71
Now multiplying the highest exponent prime factors to calculate the LCM of 161 and 168.
LCM(161,168) = 23×31×71×231
LCM(161,168) = 3864
Factors of 161
List of positive integer factors of 161 that divides 161 without a remainder.
1, 7, 23, 161
Factors of 168
List of positive integer factors of 168 that divides 168 without a remainder.
1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 161 and 168, than apply into the LCM equation.
GCF(161,168) = 7
LCM(161,168) = ( 161 × 168) / 7
LCM(161,168) = 27048 / 7
LCM(161,168) = 3864
(i) The LCM of 168 and 161 is associative
LCM of 161 and 168 = LCM of 168 and 161
1. What is the LCM of 161 and 168?
Answer: LCM of 161 and 168 is 3864.
2. What are the Factors of 161?
Answer: Factors of 161 are 1, 7, 23, 161. There are 4 integers that are factors of 161. The greatest factor of 161 is 161.
3. What are the Factors of 168?
Answer: Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168. There are 16 integers that are factors of 168. The greatest factor of 168 is 168.
4. How to Find the LCM of 161 and 168?
Answer:
Least Common Multiple of 161 and 168 = 3864
Step 1: Find the prime factorization of 161
161 = 7 x 23
Step 2: Find the prime factorization of 168
168 = 2 x 2 x 2 x 3 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3864 = 2 x 2 x 2 x 3 x 7 x 23
Step 4: Therefore, the least common multiple of 161 and 168 is 3864.