Least Common Multiple (LCM) of 120 and 34
The least common multiple (LCM) of 120 and 34 is 2040.
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 120 and 34?
First, calculate the GCD of 120 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 34 = 3 remainder 18 |
| 2 | 34 ÷ 18 = 1 remainder 16 |
| 3 | 18 ÷ 16 = 1 remainder 2 |
| 4 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 44 and 12 | 132 |
| 184 and 86 | 7912 |
| 47 and 71 | 3337 |
| 109 and 133 | 14497 |
| 71 and 140 | 9940 |