Least Common Multiple (LCM) of 140 and 106
The least common multiple (LCM) of 140 and 106 is 7420.
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 106?
First, calculate the GCD of 140 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 106 = 1 remainder 34 |
| 2 | 106 ÷ 34 = 3 remainder 4 |
| 3 | 34 ÷ 4 = 8 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 65 | 1430 |
| 114 and 185 | 21090 |
| 30 and 139 | 4170 |
| 185 and 165 | 6105 |
| 140 and 99 | 13860 |