Least Common Multiple (LCM) of 105 and 140
The least common multiple (LCM) of 105 and 140 is 420.
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 105 and 140?
First, calculate the GCD of 105 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 140 = 0 remainder 105 |
| 2 | 140 ÷ 105 = 1 remainder 35 |
| 3 | 105 ÷ 35 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 157 | 12560 |
| 121 and 197 | 23837 |
| 84 and 22 | 924 |
| 195 and 119 | 23205 |
| 118 and 174 | 10266 |