Least Common Multiple (LCM) of 186 and 72
The least common multiple (LCM) of 186 and 72 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 186 and 72?
First, calculate the GCD of 186 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 72 = 2 remainder 42 |
| 2 | 72 ÷ 42 = 1 remainder 30 |
| 3 | 42 ÷ 30 = 1 remainder 12 |
| 4 | 30 ÷ 12 = 2 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 20 | 1660 |
| 161 and 47 | 7567 |
| 174 and 70 | 6090 |
| 138 and 108 | 2484 |
| 88 and 190 | 8360 |