Least Common Multiple (LCM) of 59 and 78
The least common multiple (LCM) of 59 and 78 is 4602.
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 78?
First, calculate the GCD of 59 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 78 = 0 remainder 59 |
| 2 | 78 ÷ 59 = 1 remainder 19 |
| 3 | 59 ÷ 19 = 3 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 150 | 7350 |
| 82 and 157 | 12874 |
| 194 and 180 | 17460 |
| 33 and 15 | 165 |
| 45 and 30 | 90 |