Least Common Multiple (LCM) of 10 and 37
The least common multiple (LCM) of 10 and 37 is 370.
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 10 and 37?
First, calculate the GCD of 10 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 10 ÷ 37 = 0 remainder 10 |
| 2 | 37 ÷ 10 = 3 remainder 7 |
| 3 | 10 ÷ 7 = 1 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 45 | 1440 |
| 112 and 145 | 16240 |
| 113 and 147 | 16611 |
| 133 and 47 | 6251 |
| 149 and 175 | 26075 |