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 |
|---|---|
| 40 and 105 | 840 |
| 40 and 150 | 600 |
| 89 and 148 | 13172 |
| 33 and 160 | 5280 |
| 179 and 103 | 18437 |