Least Common Multiple (LCM) of 140 and 105
The least common multiple (LCM) of 140 and 105 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 140 and 105?
First, calculate the GCD of 140 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 105 = 1 remainder 35 |
| 2 | 105 ÷ 35 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 103 | 5562 |
| 81 and 197 | 15957 |
| 17 and 111 | 1887 |
| 149 and 10 | 1490 |
| 100 and 109 | 10900 |