Least Common Multiple (LCM) of 21 and 143
The least common multiple (LCM) of 21 and 143 is 3003.
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 143?
First, calculate the GCD of 21 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 143 = 0 remainder 21 |
| 2 | 143 ÷ 21 = 6 remainder 17 |
| 3 | 21 ÷ 17 = 1 remainder 4 |
| 4 | 17 ÷ 4 = 4 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 93 | 4929 |
| 156 and 140 | 5460 |
| 160 and 42 | 3360 |
| 93 and 129 | 3999 |
| 170 and 40 | 680 |