Least Common Multiple (LCM) of 186 and 113
The least common multiple (LCM) of 186 and 113 is 21018.
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 186 and 113?
First, calculate the GCD of 186 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 113 = 1 remainder 73 |
| 2 | 113 ÷ 73 = 1 remainder 40 |
| 3 | 73 ÷ 40 = 1 remainder 33 |
| 4 | 40 ÷ 33 = 1 remainder 7 |
| 5 | 33 ÷ 7 = 4 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 26 and 102 | 1326 |
| 115 and 155 | 3565 |
| 74 and 128 | 4736 |
| 44 and 182 | 4004 |
| 175 and 138 | 24150 |