Least Common Multiple (LCM) of 21 and 145
The least common multiple (LCM) of 21 and 145 is 3045.
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 21 and 145?
First, calculate the GCD of 21 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 145 = 0 remainder 21 |
| 2 | 145 ÷ 21 = 6 remainder 19 |
| 3 | 21 ÷ 19 = 1 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 112 | 4144 |
| 180 and 138 | 4140 |
| 67 and 61 | 4087 |
| 133 and 24 | 3192 |
| 16 and 39 | 624 |