Least Common Multiple (LCM) of 51 and 169
The least common multiple (LCM) of 51 and 169 is 8619.
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 51 and 169?
First, calculate the GCD of 51 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 169 = 0 remainder 51 |
| 2 | 169 ÷ 51 = 3 remainder 16 |
| 3 | 51 ÷ 16 = 3 remainder 3 |
| 4 | 16 ÷ 3 = 5 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 79 | 13351 |
| 99 and 119 | 11781 |
| 55 and 68 | 3740 |
| 56 and 162 | 4536 |
| 49 and 199 | 9751 |