Least Common Multiple (LCM) of 120 and 169
The least common multiple (LCM) of 120 and 169 is 20280.
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 120 and 169?
First, calculate the GCD of 120 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 169 = 0 remainder 120 |
| 2 | 169 ÷ 120 = 1 remainder 49 |
| 3 | 120 ÷ 49 = 2 remainder 22 |
| 4 | 49 ÷ 22 = 2 remainder 5 |
| 5 | 22 ÷ 5 = 4 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 106 | 13886 |
| 25 and 23 | 575 |
| 125 and 42 | 5250 |
| 92 and 186 | 8556 |
| 29 and 96 | 2784 |