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 |
|---|---|
| 169 and 112 | 18928 |
| 153 and 108 | 1836 |
| 85 and 31 | 2635 |
| 76 and 126 | 4788 |
| 74 and 134 | 4958 |