Least Common Multiple (LCM) of 21 and 119
The least common multiple (LCM) of 21 and 119 is 357.
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 119?
First, calculate the GCD of 21 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 119 = 0 remainder 21 |
| 2 | 119 ÷ 21 = 5 remainder 14 |
| 3 | 21 ÷ 14 = 1 remainder 7 |
| 4 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 137 | 18906 |
| 89 and 101 | 8989 |
| 17 and 86 | 1462 |
| 152 and 86 | 6536 |
| 113 and 40 | 4520 |