Least Common Multiple (LCM) of 113 and 143
The least common multiple (LCM) of 113 and 143 is 16159.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 113 and 143?
First, calculate the GCD of 113 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 143 = 0 remainder 113 |
| 2 | 143 ÷ 113 = 1 remainder 30 |
| 3 | 113 ÷ 30 = 3 remainder 23 |
| 4 | 30 ÷ 23 = 1 remainder 7 |
| 5 | 23 ÷ 7 = 3 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 196 | 6076 |
| 111 and 137 | 15207 |
| 58 and 113 | 6554 |
| 151 and 25 | 3775 |
| 66 and 190 | 6270 |