Least Common Multiple (LCM) of 140 and 169
The least common multiple (LCM) of 140 and 169 is 23660.
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 169?
First, calculate the GCD of 140 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 169 = 0 remainder 140 |
| 2 | 169 ÷ 140 = 1 remainder 29 |
| 3 | 140 ÷ 29 = 4 remainder 24 |
| 4 | 29 ÷ 24 = 1 remainder 5 |
| 5 | 24 ÷ 5 = 4 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 77 | 9933 |
| 181 and 200 | 36200 |
| 137 and 83 | 11371 |
| 140 and 101 | 14140 |
| 148 and 41 | 6068 |