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 70 the smallest integer that is 1890 that is divisible by both numbers.
Least Common Multiple (LCM) of 54 and 70 is 1890.
LCM(54,70) = 1890
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 70. First we will calculate the prime factors of 54 and 70.
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 70
2 | 70 |
5 | 35 |
7 | 7 |
1 |
Prime factors of 70 are 2, 5,7. Prime factorization of 70 in exponential form is:
70 = 21×51×71
Now multiplying the highest exponent prime factors to calculate the LCM of 54 and 70.
LCM(54,70) = 21×33×51×71
LCM(54,70) = 1890
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 70
List of positive integer factors of 70 that divides 70 without a remainder.
1, 2, 5, 7, 10, 14, 35, 70
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54 and 70, than apply into the LCM equation.
GCF(54,70) = 2
LCM(54,70) = ( 54 × 70) / 2
LCM(54,70) = 3780 / 2
LCM(54,70) = 1890
(i) The LCM of 70 and 54 is associative
LCM of 54 and 70 = LCM of 70 and 54
1. What is the LCM of 54 and 70?
Answer: LCM of 54 and 70 is 1890.
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 70?
Answer: Factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70. There are 8 integers that are factors of 70. The greatest factor of 70 is 70.
4. How to Find the LCM of 54 and 70?
Answer:
Least Common Multiple of 54 and 70 = 1890
Step 1: Find the prime factorization of 54
54 = 2 x 3 x 3 x 3
Step 2: Find the prime factorization of 70
70 = 2 x 5 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1890 = 2 x 3 x 3 x 3 x 5 x 7
Step 4: Therefore, the least common multiple of 54 and 70 is 1890.