Least Common Multiple (LCM) of 99 and 160
The least common multiple (LCM) of 99 and 160 is 15840.
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 160?
First, calculate the GCD of 99 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 160 = 0 remainder 99 |
| 2 | 160 ÷ 99 = 1 remainder 61 |
| 3 | 99 ÷ 61 = 1 remainder 38 |
| 4 | 61 ÷ 38 = 1 remainder 23 |
| 5 | 38 ÷ 23 = 1 remainder 15 |
| 6 | 23 ÷ 15 = 1 remainder 8 |
| 7 | 15 ÷ 8 = 1 remainder 7 |
| 8 | 8 ÷ 7 = 1 remainder 1 |
| 9 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 156 | 5148 |
| 174 and 181 | 31494 |
| 112 and 67 | 7504 |
| 105 and 127 | 13335 |
| 11 and 174 | 1914 |