Least Common Multiple (LCM) of 21 and 102
The least common multiple (LCM) of 21 and 102 is 714.
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 102?
First, calculate the GCD of 21 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 102 = 0 remainder 21 |
| 2 | 102 ÷ 21 = 4 remainder 18 |
| 3 | 21 ÷ 18 = 1 remainder 3 |
| 4 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 43 | 6493 |
| 13 and 119 | 1547 |
| 29 and 61 | 1769 |
| 114 and 154 | 8778 |
| 197 and 19 | 3743 |