Least Common Multiple (LCM) of 96 and 137
The least common multiple (LCM) of 96 and 137 is 13152.
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 137?
First, calculate the GCD of 96 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 137 = 0 remainder 96 |
| 2 | 137 ÷ 96 = 1 remainder 41 |
| 3 | 96 ÷ 41 = 2 remainder 14 |
| 4 | 41 ÷ 14 = 2 remainder 13 |
| 5 | 14 ÷ 13 = 1 remainder 1 |
| 6 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 182 | 13832 |
| 58 and 38 | 1102 |
| 69 and 73 | 5037 |
| 73 and 66 | 4818 |
| 26 and 45 | 1170 |