Least Common Multiple (LCM) of 37 and 104
The least common multiple (LCM) of 37 and 104 is 3848.
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 37 and 104?
First, calculate the GCD of 37 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 104 = 0 remainder 37 |
| 2 | 104 ÷ 37 = 2 remainder 30 |
| 3 | 37 ÷ 30 = 1 remainder 7 |
| 4 | 30 ÷ 7 = 4 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 27 | 108 |
| 122 and 132 | 8052 |
| 138 and 150 | 3450 |
| 38 and 74 | 1406 |
| 151 and 172 | 25972 |