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 |
|---|---|
| 151 and 28 | 4228 |
| 136 and 197 | 26792 |
| 190 and 125 | 4750 |
| 48 and 193 | 9264 |
| 162 and 40 | 3240 |