Least Common Multiple (LCM) of 169 and 120
The least common multiple (LCM) of 169 and 120 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 169 and 120?
First, calculate the GCD of 169 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 120 = 1 remainder 49 |
| 2 | 120 ÷ 49 = 2 remainder 22 |
| 3 | 49 ÷ 22 = 2 remainder 5 |
| 4 | 22 ÷ 5 = 4 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 132 | 4488 |
| 106 and 55 | 5830 |
| 69 and 32 | 2208 |
| 137 and 163 | 22331 |
| 161 and 33 | 5313 |