Least Common Multiple (LCM) of 78 and 140
The least common multiple (LCM) of 78 and 140 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 78 and 140?
First, calculate the GCD of 78 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 140 = 0 remainder 78 |
| 2 | 140 ÷ 78 = 1 remainder 62 |
| 3 | 78 ÷ 62 = 1 remainder 16 |
| 4 | 62 ÷ 16 = 3 remainder 14 |
| 5 | 16 ÷ 14 = 1 remainder 2 |
| 6 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 138 | 8970 |
| 196 and 109 | 21364 |
| 56 and 186 | 5208 |
| 189 and 172 | 32508 |
| 13 and 145 | 1885 |