Least Common Multiple (LCM) of 59 and 160
The least common multiple (LCM) of 59 and 160 is 9440.
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 59 and 160?
First, calculate the GCD of 59 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 160 = 0 remainder 59 |
| 2 | 160 ÷ 59 = 2 remainder 42 |
| 3 | 59 ÷ 42 = 1 remainder 17 |
| 4 | 42 ÷ 17 = 2 remainder 8 |
| 5 | 17 ÷ 8 = 2 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 132 | 5412 |
| 115 and 30 | 690 |
| 59 and 145 | 8555 |
| 15 and 42 | 210 |
| 31 and 175 | 5425 |