Least Common Multiple (LCM) of 186 and 123
The least common multiple (LCM) of 186 and 123 is 7626.
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 123?
First, calculate the GCD of 186 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 123 = 1 remainder 63 |
| 2 | 123 ÷ 63 = 1 remainder 60 |
| 3 | 63 ÷ 60 = 1 remainder 3 |
| 4 | 60 ÷ 3 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 74 | 370 |
| 92 and 159 | 14628 |
| 178 and 192 | 17088 |
| 162 and 102 | 2754 |
| 166 and 154 | 12782 |