Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 3 and 23 the smallest integer that is 69 that is divisible by both numbers.
Least Common Multiple (LCM) of 3 and 23 is 69.
LCM(3,23) = 69
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 23. First we will calculate the prime factors of 3 and 23.
Prime Factorization of 3
3 | 3 |
1 |
Prime factors of 3 are 3. Prime factorization of 3 in exponential form is:
3 = 31
Prime Factorization of 23
23 | 23 |
1 |
Prime factors of 23 are 23. Prime factorization of 23 in exponential form is:
23 = 231
Now multiplying the highest exponent prime factors to calculate the LCM of 3 and 23.
LCM(3,23) = 31×231
LCM(3,23) = 69
Factors of 3
List of positive integer factors of 3 that divides 3 without a remainder.
1, 3
Factors of 23
List of positive integer factors of 23 that divides 23 without a remainder.
1, 23
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3 and 23, than apply into the LCM equation.
GCF(3,23) = 1
LCM(3,23) = ( 3 × 23) / 1
LCM(3,23) = 69 / 1
LCM(3,23) = 69
(i) The LCM of 23 and 3 is associative
LCM of 3 and 23 = LCM of 23 and 3
1. What is the LCM of 3 and 23?
Answer: LCM of 3 and 23 is 69.
2. What are the Factors of 3?
Answer: Factors of 3 are 1, 3. There are 2 integers that are factors of 3. The greatest factor of 3 is 3.
3. What are the Factors of 23?
Answer: Factors of 23 are 1, 23. There are 2 integers that are factors of 23. The greatest factor of 23 is 23.
4. How to Find the LCM of 3 and 23?
Answer:
Least Common Multiple of 3 and 23 = 69
Step 1: Find the prime factorization of 3
3 = 3
Step 2: Find the prime factorization of 23
23 = 23
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 69 = 3 x 23
Step 4: Therefore, the least common multiple of 3 and 23 is 69.