Least Common Multiple (LCM) of 60 and 34
The least common multiple (LCM) of 60 and 34 is 1020.
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 60 and 34?
First, calculate the GCD of 60 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 34 = 1 remainder 26 |
| 2 | 34 ÷ 26 = 1 remainder 8 |
| 3 | 26 ÷ 8 = 3 remainder 2 |
| 4 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 84 | 1344 |
| 105 and 54 | 1890 |
| 106 and 154 | 8162 |
| 178 and 132 | 11748 |
| 125 and 188 | 23500 |