Least Common Multiple (LCM) of 169 and 137
The least common multiple (LCM) of 169 and 137 is 23153.
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 137?
First, calculate the GCD of 169 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 137 = 1 remainder 32 |
| 2 | 137 ÷ 32 = 4 remainder 9 |
| 3 | 32 ÷ 9 = 3 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 74 | 3922 |
| 198 and 67 | 13266 |
| 60 and 107 | 6420 |
| 111 and 139 | 15429 |
| 186 and 137 | 25482 |