Least Common Multiple (LCM) of 113 and 157
The least common multiple (LCM) of 113 and 157 is 17741.
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 157?
First, calculate the GCD of 113 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 157 = 0 remainder 113 |
| 2 | 157 ÷ 113 = 1 remainder 44 |
| 3 | 113 ÷ 44 = 2 remainder 25 |
| 4 | 44 ÷ 25 = 1 remainder 19 |
| 5 | 25 ÷ 19 = 1 remainder 6 |
| 6 | 19 ÷ 6 = 3 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 144 | 5328 |
| 83 and 132 | 10956 |
| 162 and 189 | 1134 |
| 35 and 29 | 1015 |
| 105 and 87 | 3045 |