Least Common Multiple (LCM) of 160 and 99
The least common multiple (LCM) of 160 and 99 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 160 and 99?
First, calculate the GCD of 160 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 99 = 1 remainder 61 |
| 2 | 99 ÷ 61 = 1 remainder 38 |
| 3 | 61 ÷ 38 = 1 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 |
|---|---|
| 69 and 195 | 4485 |
| 51 and 194 | 9894 |
| 36 and 58 | 1044 |
| 111 and 35 | 3885 |
| 27 and 41 | 1107 |