Least Common Multiple (LCM) of 160 and 117
The least common multiple (LCM) of 160 and 117 is 18720.
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 117?
First, calculate the GCD of 160 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 117 = 1 remainder 43 |
| 2 | 117 ÷ 43 = 2 remainder 31 |
| 3 | 43 ÷ 31 = 1 remainder 12 |
| 4 | 31 ÷ 12 = 2 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 168 | 4200 |
| 185 and 147 | 27195 |
| 148 and 128 | 4736 |
| 178 and 100 | 8900 |
| 104 and 10 | 520 |