Least Common Multiple (LCM) of 59 and 157
The least common multiple (LCM) of 59 and 157 is 9263.
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 157?
First, calculate the GCD of 59 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 157 = 0 remainder 59 |
| 2 | 157 ÷ 59 = 2 remainder 39 |
| 3 | 59 ÷ 39 = 1 remainder 20 |
| 4 | 39 ÷ 20 = 1 remainder 19 |
| 5 | 20 ÷ 19 = 1 remainder 1 |
| 6 | 19 ÷ 1 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 14 | 1260 |
| 59 and 117 | 6903 |
| 162 and 80 | 6480 |
| 13 and 109 | 1417 |
| 143 and 132 | 1716 |