Least Common Multiple (LCM) of 140 and 78
The least common multiple (LCM) of 140 and 78 is 5460.
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 140 and 78?
First, calculate the GCD of 140 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 78 = 1 remainder 62 |
| 2 | 78 ÷ 62 = 1 remainder 16 |
| 3 | 62 ÷ 16 = 3 remainder 14 |
| 4 | 16 ÷ 14 = 1 remainder 2 |
| 5 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 178 | 21894 |
| 15 and 174 | 870 |
| 12 and 113 | 1356 |
| 95 and 119 | 11305 |
| 180 and 83 | 14940 |