Least Common Multiple (LCM) of 135 and 169
The least common multiple (LCM) of 135 and 169 is 22815.
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 135 and 169?
First, calculate the GCD of 135 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 169 = 0 remainder 135 |
| 2 | 169 ÷ 135 = 1 remainder 34 |
| 3 | 135 ÷ 34 = 3 remainder 33 |
| 4 | 34 ÷ 33 = 1 remainder 1 |
| 5 | 33 ÷ 1 = 33 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 87 | 1218 |
| 177 and 15 | 885 |
| 37 and 61 | 2257 |
| 161 and 142 | 22862 |
| 119 and 117 | 13923 |