Least Common Multiple (LCM) of 59 and 142
The least common multiple (LCM) of 59 and 142 is 8378.
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 142?
First, calculate the GCD of 59 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 142 = 0 remainder 59 |
| 2 | 142 ÷ 59 = 2 remainder 24 |
| 3 | 59 ÷ 24 = 2 remainder 11 |
| 4 | 24 ÷ 11 = 2 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 99 | 1881 |
| 88 and 98 | 4312 |
| 188 and 65 | 12220 |
| 179 and 100 | 17900 |
| 16 and 155 | 2480 |