Least Common Multiple (LCM) of 96 and 169
The least common multiple (LCM) of 96 and 169 is 16224.
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 96 and 169?
First, calculate the GCD of 96 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 169 = 0 remainder 96 |
| 2 | 169 ÷ 96 = 1 remainder 73 |
| 3 | 96 ÷ 73 = 1 remainder 23 |
| 4 | 73 ÷ 23 = 3 remainder 4 |
| 5 | 23 ÷ 4 = 5 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 199 | 36815 |
| 86 and 117 | 10062 |
| 142 and 61 | 8662 |
| 88 and 95 | 8360 |
| 75 and 81 | 2025 |