Least Common Multiple (LCM) of 21 and 58
The least common multiple (LCM) of 21 and 58 is 1218.
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 58?
First, calculate the GCD of 21 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 58 = 0 remainder 21 |
| 2 | 58 ÷ 21 = 2 remainder 16 |
| 3 | 21 ÷ 16 = 1 remainder 5 |
| 4 | 16 ÷ 5 = 3 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 33 | 1947 |
| 182 and 23 | 4186 |
| 83 and 81 | 6723 |
| 114 and 75 | 2850 |
| 149 and 67 | 9983 |