Least Common Multiple (LCM) of 186 and 73
The least common multiple (LCM) of 186 and 73 is 13578.
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 73?
First, calculate the GCD of 186 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 73 = 2 remainder 40 |
| 2 | 73 ÷ 40 = 1 remainder 33 |
| 3 | 40 ÷ 33 = 1 remainder 7 |
| 4 | 33 ÷ 7 = 4 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 35 | 1120 |
| 79 and 22 | 1738 |
| 35 and 104 | 3640 |
| 184 and 32 | 736 |
| 53 and 180 | 9540 |