Least Common Multiple (LCM) of 114 and 36
The least common multiple (LCM) of 114 and 36 is 684.
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 114 and 36?
First, calculate the GCD of 114 and 36 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 36 = 3 remainder 6 |
| 2 | 36 ÷ 6 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 64 | 1600 |
| 49 and 125 | 6125 |
| 121 and 112 | 13552 |
| 92 and 50 | 2300 |
| 107 and 35 | 3745 |