Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 140 and 143 the smallest integer that is 20020 that is divisible by both numbers.
Least Common Multiple (LCM) of 140 and 143 is 20020.
LCM(140,143) = 20020
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 140 and 143. First we will calculate the prime factors of 140 and 143.
Prime Factorization of 140
2 | 140 |
2 | 70 |
5 | 35 |
7 | 7 |
1 |
Prime factors of 140 are 2, 5,7. Prime factorization of 140 in exponential form is:
140 = 22×51×71
Prime Factorization of 143
11 | 143 |
13 | 13 |
1 |
Prime factors of 143 are 11,13. Prime factorization of 143 in exponential form is:
143 = 111×131
Now multiplying the highest exponent prime factors to calculate the LCM of 140 and 143.
LCM(140,143) = 22×51×71×111×131
LCM(140,143) = 20020
Factors of 140
List of positive integer factors of 140 that divides 140 without a remainder.
1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
Factors of 143
List of positive integer factors of 143 that divides 143 without a remainder.
1, 11, 13, 143
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 140 and 143, than apply into the LCM equation.
GCF(140,143) = 1
LCM(140,143) = ( 140 × 143) / 1
LCM(140,143) = 20020 / 1
LCM(140,143) = 20020
(i) The LCM of 143 and 140 is associative
LCM of 140 and 143 = LCM of 143 and 140
1. What is the LCM of 140 and 143?
Answer: LCM of 140 and 143 is 20020.
2. What are the Factors of 140?
Answer: Factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140. There are 12 integers that are factors of 140. The greatest factor of 140 is 140.
3. What are the Factors of 143?
Answer: Factors of 143 are 1, 11, 13, 143. There are 4 integers that are factors of 143. The greatest factor of 143 is 143.
4. How to Find the LCM of 140 and 143?
Answer:
Least Common Multiple of 140 and 143 = 20020
Step 1: Find the prime factorization of 140
140 = 2 x 2 x 5 x 7
Step 2: Find the prime factorization of 143
143 = 11 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 20020 = 2 x 2 x 5 x 7 x 11 x 13
Step 4: Therefore, the least common multiple of 140 and 143 is 20020.