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 |
|---|---|
| 52 and 139 | 7228 |
| 192 and 163 | 31296 |
| 179 and 63 | 11277 |
| 168 and 103 | 17304 |
| 73 and 112 | 8176 |