Least Common Multiple (LCM) of 48 and 169
The least common multiple (LCM) of 48 and 169 is 8112.
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 48 and 169?
First, calculate the GCD of 48 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 169 = 0 remainder 48 |
| 2 | 169 ÷ 48 = 3 remainder 25 |
| 3 | 48 ÷ 25 = 1 remainder 23 |
| 4 | 25 ÷ 23 = 1 remainder 2 |
| 5 | 23 ÷ 2 = 11 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 53 | 159 |
| 80 and 111 | 8880 |
| 174 and 169 | 29406 |
| 151 and 135 | 20385 |
| 105 and 188 | 19740 |