Least Common Multiple (LCM) of 78 and 117
The least common multiple (LCM) of 78 and 117 is 234.
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 78 and 117?
First, calculate the GCD of 78 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 117 = 0 remainder 78 |
| 2 | 117 ÷ 78 = 1 remainder 39 |
| 3 | 78 ÷ 39 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 118 | 19706 |
| 117 and 109 | 12753 |
| 142 and 28 | 1988 |
| 172 and 50 | 4300 |
| 20 and 121 | 2420 |