Least Common Multiple (LCM) of 117 and 169
The least common multiple (LCM) of 117 and 169 is 1521.
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 117 and 169?
First, calculate the GCD of 117 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 169 = 0 remainder 117 |
| 2 | 169 ÷ 117 = 1 remainder 52 |
| 3 | 117 ÷ 52 = 2 remainder 13 |
| 4 | 52 ÷ 13 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 137 | 26441 |
| 114 and 92 | 5244 |
| 35 and 156 | 5460 |
| 98 and 36 | 1764 |
| 78 and 82 | 3198 |