Least Common Multiple (LCM) of 21 and 123
The least common multiple (LCM) of 21 and 123 is 861.
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 123?
First, calculate the GCD of 21 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 123 = 0 remainder 21 |
| 2 | 123 ÷ 21 = 5 remainder 18 |
| 3 | 21 ÷ 18 = 1 remainder 3 |
| 4 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 89 | 13172 |
| 114 and 160 | 9120 |
| 45 and 70 | 630 |
| 60 and 167 | 10020 |
| 157 and 178 | 27946 |