Least Common Multiple (LCM) of 36 and 123
The least common multiple (LCM) of 36 and 123 is 1476.
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 36 and 123?
First, calculate the GCD of 36 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 123 = 0 remainder 36 |
| 2 | 123 ÷ 36 = 3 remainder 15 |
| 3 | 36 ÷ 15 = 2 remainder 6 |
| 4 | 15 ÷ 6 = 2 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 20 | 2340 |
| 189 and 119 | 3213 |
| 92 and 165 | 15180 |
| 82 and 121 | 9922 |
| 196 and 137 | 26852 |