Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 54 and 71 the smallest integer that is 3834 that is divisible by both numbers.
Least Common Multiple (LCM) of 54 and 71 is 3834.
LCM(54,71) = 3834
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 54 and 71. First we will calculate the prime factors of 54 and 71.
Prime Factorization of 54
2 | 54 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
Prime factors of 54 are 2,3. Prime factorization of 54 in exponential form is:
54 = 21×33
Prime Factorization of 71
71 | 71 |
1 |
Prime factors of 71 are 71. Prime factorization of 71 in exponential form is:
71 = 711
Now multiplying the highest exponent prime factors to calculate the LCM of 54 and 71.
LCM(54,71) = 21×33×711
LCM(54,71) = 3834
Factors of 54
List of positive integer factors of 54 that divides 54 without a remainder.
1, 2, 3, 6, 9, 18, 27, 54
Factors of 71
List of positive integer factors of 71 that divides 71 without a remainder.
1, 71
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54 and 71, than apply into the LCM equation.
GCF(54,71) = 1
LCM(54,71) = ( 54 × 71) / 1
LCM(54,71) = 3834 / 1
LCM(54,71) = 3834
(i) The LCM of 71 and 54 is associative
LCM of 54 and 71 = LCM of 71 and 54
1. What is the LCM of 54 and 71?
Answer: LCM of 54 and 71 is 3834.
2. What are the Factors of 54?
Answer: Factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54. There are 8 integers that are factors of 54. The greatest factor of 54 is 54.
3. What are the Factors of 71?
Answer: Factors of 71 are 1, 71. There are 2 integers that are factors of 71. The greatest factor of 71 is 71.
4. How to Find the LCM of 54 and 71?
Answer:
Least Common Multiple of 54 and 71 = 3834
Step 1: Find the prime factorization of 54
54 = 2 x 3 x 3 x 3
Step 2: Find the prime factorization of 71
71 = 71
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3834 = 2 x 3 x 3 x 3 x 71
Step 4: Therefore, the least common multiple of 54 and 71 is 3834.