Least Common Multiple (LCM) of 21 and 149
The least common multiple (LCM) of 21 and 149 is 3129.
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 149?
First, calculate the GCD of 21 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 149 = 0 remainder 21 |
| 2 | 149 ÷ 21 = 7 remainder 2 |
| 3 | 21 ÷ 2 = 10 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 23 | 3220 |
| 13 and 39 | 39 |
| 166 and 65 | 10790 |
| 47 and 53 | 2491 |
| 141 and 13 | 1833 |