Least Common Multiple (LCM) of 123 and 21
The least common multiple (LCM) of 123 and 21 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 123 and 21?
First, calculate the GCD of 123 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 21 = 5 remainder 18 |
| 2 | 21 ÷ 18 = 1 remainder 3 |
| 3 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 169 | 507 |
| 23 and 160 | 3680 |
| 195 and 176 | 34320 |
| 99 and 156 | 5148 |
| 185 and 117 | 21645 |