Least Common Multiple (LCM) of 96 and 149
The least common multiple (LCM) of 96 and 149 is 14304.
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 149?
First, calculate the GCD of 96 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 149 = 0 remainder 96 |
| 2 | 149 ÷ 96 = 1 remainder 53 |
| 3 | 96 ÷ 53 = 1 remainder 43 |
| 4 | 53 ÷ 43 = 1 remainder 10 |
| 5 | 43 ÷ 10 = 4 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 79 and 95 | 7505 |
| 88 and 199 | 17512 |
| 115 and 169 | 19435 |
| 179 and 110 | 19690 |
| 100 and 122 | 6100 |