Least Common Multiple (LCM) of 99 and 137
The least common multiple (LCM) of 99 and 137 is 13563.
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 99 and 137?
First, calculate the GCD of 99 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 137 = 0 remainder 99 |
| 2 | 137 ÷ 99 = 1 remainder 38 |
| 3 | 99 ÷ 38 = 2 remainder 23 |
| 4 | 38 ÷ 23 = 1 remainder 15 |
| 5 | 23 ÷ 15 = 1 remainder 8 |
| 6 | 15 ÷ 8 = 1 remainder 7 |
| 7 | 8 ÷ 7 = 1 remainder 1 |
| 8 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 56 | 4760 |
| 67 and 98 | 6566 |
| 150 and 106 | 7950 |
| 11 and 145 | 1595 |
| 168 and 52 | 2184 |