Least Common Multiple (LCM) of 34 and 37
The least common multiple (LCM) of 34 and 37 is 1258.
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 34 and 37?
First, calculate the GCD of 34 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 37 = 0 remainder 34 |
| 2 | 37 ÷ 34 = 1 remainder 3 |
| 3 | 34 ÷ 3 = 11 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 75 | 1275 |
| 153 and 116 | 17748 |
| 132 and 173 | 22836 |
| 190 and 126 | 11970 |
| 112 and 192 | 1344 |