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 |
|---|---|
| 174 and 12 | 348 |
| 137 and 56 | 7672 |
| 190 and 18 | 1710 |
| 131 and 76 | 9956 |
| 165 and 62 | 10230 |