Least Common Multiple (LCM) of 72 and 186
The least common multiple (LCM) of 72 and 186 is 2232.
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 72 and 186?
First, calculate the GCD of 72 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 186 = 0 remainder 72 |
| 2 | 186 ÷ 72 = 2 remainder 42 |
| 3 | 72 ÷ 42 = 1 remainder 30 |
| 4 | 42 ÷ 30 = 1 remainder 12 |
| 5 | 30 ÷ 12 = 2 remainder 6 |
| 6 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 142 | 1562 |
| 173 and 80 | 13840 |
| 142 and 29 | 4118 |
| 59 and 15 | 885 |
| 20 and 77 | 1540 |