Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 160 and 180 the smallest integer that is 1440 that is divisible by both numbers.
Least Common Multiple (LCM) of 160 and 180 is 1440.
LCM(160,180) = 1440
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 160 and 180. First we will calculate the prime factors of 160 and 180.
Prime Factorization of 160
2 | 160 |
2 | 80 |
2 | 40 |
2 | 20 |
2 | 10 |
5 | 5 |
1 |
Prime factors of 160 are 2,5. Prime factorization of 160 in exponential form is:
160 = 25×51
Prime Factorization of 180
2 | 180 |
2 | 90 |
3 | 45 |
3 | 15 |
5 | 5 |
1 |
Prime factors of 180 are 2, 3,5. Prime factorization of 180 in exponential form is:
180 = 22×32×51
Now multiplying the highest exponent prime factors to calculate the LCM of 160 and 180.
LCM(160,180) = 25×32×51
LCM(160,180) = 1440
Factors of 160
List of positive integer factors of 160 that divides 160 without a remainder.
1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
Factors of 180
List of positive integer factors of 180 that divides 180 without a remainder.
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 160 and 180, than apply into the LCM equation.
GCF(160,180) = 20
LCM(160,180) = ( 160 × 180) / 20
LCM(160,180) = 28800 / 20
LCM(160,180) = 1440
(i) The LCM of 180 and 160 is associative
LCM of 160 and 180 = LCM of 180 and 160
1. What is the LCM of 160 and 180?
Answer: LCM of 160 and 180 is 1440.
2. What are the Factors of 160?
Answer: Factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160. There are 12 integers that are factors of 160. The greatest factor of 160 is 160.
3. What are the Factors of 180?
Answer: Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180. There are 18 integers that are factors of 180. The greatest factor of 180 is 180.
4. How to Find the LCM of 160 and 180?
Answer:
Least Common Multiple of 160 and 180 = 1440
Step 1: Find the prime factorization of 160
160 = 2 x 2 x 2 x 2 x 2 x 5
Step 2: Find the prime factorization of 180
180 = 2 x 2 x 3 x 3 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1440 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5
Step 4: Therefore, the least common multiple of 160 and 180 is 1440.