Least Common Multiple (LCM) of 106 and 37
The least common multiple (LCM) of 106 and 37 is 3922.
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 106 and 37?
First, calculate the GCD of 106 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 37 = 2 remainder 32 |
| 2 | 37 ÷ 32 = 1 remainder 5 |
| 3 | 32 ÷ 5 = 6 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 100 | 2900 |
| 116 and 167 | 19372 |
| 142 and 40 | 2840 |
| 176 and 84 | 3696 |
| 170 and 110 | 1870 |