Least Common Multiple (LCM) of 105 and 37
The least common multiple (LCM) of 105 and 37 is 3885.
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 105 and 37?
First, calculate the GCD of 105 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 37 = 2 remainder 31 |
| 2 | 37 ÷ 31 = 1 remainder 6 |
| 3 | 31 ÷ 6 = 5 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 66 | 9570 |
| 169 and 175 | 29575 |
| 104 and 72 | 936 |
| 131 and 165 | 21615 |
| 36 and 113 | 4068 |