Least Common Multiple (LCM) of 187 and 113
The least common multiple (LCM) of 187 and 113 is 21131.
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 187 and 113?
First, calculate the GCD of 187 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 113 = 1 remainder 74 |
| 2 | 113 ÷ 74 = 1 remainder 39 |
| 3 | 74 ÷ 39 = 1 remainder 35 |
| 4 | 39 ÷ 35 = 1 remainder 4 |
| 5 | 35 ÷ 4 = 8 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 62 | 9362 |
| 56 and 124 | 1736 |
| 121 and 64 | 7744 |
| 109 and 105 | 11445 |
| 96 and 100 | 2400 |