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545 LearnersLast updated on August 5, 2025
LCM of 19 and 57
LCM of 19 and 57
The LCM of 19 and 57 is 57. The LCM can be ascertained using anyone from the three methods discussed below.
LCM of 19 and 57 Using Prime Factorization
Prime factorize the numbers
19 = 19 — it is a prime number
57 = 19×3
Multiply the highest powers
19×3
LCM(19,57) = 57
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LCM of [Topic] Using Division Method
- Write the numbers in a row
- Divide them by their common prime factors
- Carry forward the numbers that are not divided by the previously chosen number
- Continue dividing until the remainder is ‘1’
- Multiply the divisors to find the LCM
- LCM (19,57) = 57
Common mistakes and How to avoid them while finding the LCM of 19 and 57
Listed here are a few mistakes that one can commit when trying to find the LCM of the numbers 19 and 57. Try to avoid them.
Mistake 1
listing incorrect multiples
if the LCM of given numbers is 57, double-check that the number appears on the list of both 19 and 57.
Mistake 2
prime factorization errors
check if the numbers are prime factored correctly. For example, we may accidentally write 57 = 19×5 instead of 57 = 19×3.
Mistake 3
One may think the product of the numbers is the LCM of the numbers. This is only true in case of co-prime numbers.
LCM of 19 and 57 Examples
Problem 1
A project needs to be completed every 19 days, and an associated report is submitted every 57 days. What percentage of the project cycle aligns with the report submission?
Total time to align both cycles: LCM(19, 57) = 57 days
Percentage of alignment = (19 ÷ 57) × 100 = 33.33%
Explanation
The project cycle aligns with the report submission every 57 days, which is 33.33% of the project cycle.
Problem 2
A machine performs an operation every 19 hours, while another machine performs its operation every 57 hours. If both machines started at the same time, when will they operate together again?
LCM(a, b) = a×b/HCF(a, b)
LCM (a, b) = 19×57/19
LCM(19, 57) = 57 hours
Explanation
Both machines will operate together again in 57 hours.
Problem 3
Verify the relationship between the LCM and HCF of 19 and 57
We apply the formula → LCM(a, b)×HCF(a, b)=a×b to check the relationship between the numbers;
LCM of 19 and 57 = 57
HCF of 19 and 57 = 19
Now, verifying the same;
LCM(a, b)×HCF(a, b)=a×b
57×19=19×57
1083=1083
Explanation
The above is how we ascertain and verify the relationship between the LCM and the HCF of two given numbers.
FAQs on Least Common Multiple of 19 and 57
1.Are 19 and 57 prime numbers?
2.Is 19 divisible by 57?
3. What is the LCM of 9 and 57?
4. Find the HCF of 19 and 57?
5.Is 990 divisible by 2?
Important Glossaries for LCM of 19 and 57
- Multiple: product of a number and integer
- Prime Factor: a number whose factors are itself and 1
- Prime Factorization: breaking a large number into its prime factors
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
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