Least Common Multiple (LCM) of 160 and 105
The least common multiple (LCM) of 160 and 105 is 3360.
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 105?
First, calculate the GCD of 160 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 105 = 1 remainder 55 |
| 2 | 105 ÷ 55 = 1 remainder 50 |
| 3 | 55 ÷ 50 = 1 remainder 5 |
| 4 | 50 ÷ 5 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 29 | 1711 |
| 162 and 57 | 3078 |
| 146 and 15 | 2190 |
| 21 and 10 | 210 |
| 90 and 97 | 8730 |