Least Common Multiple (LCM) of 30 and 59
The least common multiple (LCM) of 30 and 59 is 1770.
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 30 and 59?
First, calculate the GCD of 30 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 59 = 0 remainder 30 |
| 2 | 59 ÷ 30 = 1 remainder 29 |
| 3 | 30 ÷ 29 = 1 remainder 1 |
| 4 | 29 ÷ 1 = 29 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 48 | 2160 |
| 107 and 197 | 21079 |
| 96 and 197 | 18912 |
| 149 and 60 | 8940 |
| 197 and 70 | 13790 |