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174 LearnersLast updated on November 29th, 2024
LCM of 8 and 20
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 8 and 20. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.
What is the LCM of 8 and 20?
The LCM of 8 and 20 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations like addition and subtraction with fractions to equate the denominators.
How to find the LCM of 8 and 20?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 8 and 20 using the Listing multiples method
To ascertain the LCM, list the multiples of the integers until a common multiple is found.
Steps:
1. Writedown the multiples of each number:
Multiples of 8 = 8,16,24,32,40…
Multiples of 20 = 20,40,60,80…
2. Ascertain the smallest multiple from the listed multiples of 8 and 20.
The LCM (The Least common multiple) of 8 and 20 is 40. i.e., 40 is divisible by 8 and 20 with no reminder.
LCM of 8 and 20 using the Prime Factorization
This method involves finding the prime factors of each number and then multiplying the highest power of the prime factors to get the LCM.
Steps:
— Find the prime factors of the numbers:
- Prime factorization of 8 = 2×2×2
- Prime factorization of 20 = 2×2×5
— Take the highest power of each prime factor:
— 2,2,2,5
— Multiply the ascertained factors to get the LCM:
LCM (8,12) = 2×2×2×5 = 40
LCM of 8 and 20 using the Division Method
The Division Method involves dividing the numbers by their prime factors and multiplying the divisors to get the LCM.
Steps:
- Write down the numbers in a row;
- Divide the row of numbers by a prime number that is evenly divisible into at least one of the given numbers. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.
- The LCM of the numbers is the product of the prime numbers in the first column, i.e.,
2×2×2×5= 40
LCM (8,20) = 40
Common Mistakes and how to avoid them while finding the LCM of 8 and 20
LCM of 8 and 20 Examples
Problem 1
Trains A and B arrive every 8 minutes and 20 minutes at the station at the same time. In how long will they arrive together again?
Explanation
Problem 2
C and D meet every 8 days and 20 days, respectively. They meet today, September 1, how many days will it be before they meet again?
Explanation
Problem 3
A bakery sells apple juice and orange juice in bottles. The apple juice bottles are delivered in packs of 8, and the orange juice bottles in packs of 20. What is the least number of bottles of each type of juice that needs to be bought that they have an equal number of apple and orange juice?
Explanation
Problem 4
Mr. S has two kinds of plants that need watering. The lemon plant needs to be watered every 8 days, and the orange plant needs to be watered every 20 days. If both the plants are watered today, in how many days will Mr. S water them together again?
Explanation
FAQ’s on the LCM of 8 and 20
1.What is the LCM of 8,10 and 20?
2.What is the LCM of 8,12 and 20?
3.What is the LCM formula using the HCF?
4.Is the LCM of 8 and 20 always a multiple of their HCF?
5.What is the LCM of 8,20 and 24?
Important glossaries for the LCM of 8 and 20
- Multiple: A number and any integer multiplied.
- Prime Factor: A natural number (other than 1) that has factors that are one and itself.
- Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization.
- Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime.
- Relatively Prime Numbers: Numbers that have no common factors other than 1.
- Fraction: A representation of a part of a whole.
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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.
