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 |
|---|---|
| 82 and 121 | 9922 |
| 110 and 81 | 8910 |
| 113 and 149 | 16837 |
| 92 and 189 | 17388 |
| 122 and 123 | 15006 |