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152 LearnersLast updated on November 29th, 2024
LCM of 2,4, and 7
LCM is the smallest number which can be exactly divisible by each number. It can also be defined as the least number, which is a common multiple of all 2,4,7. In practical life, LCM helps to find out when an event will occur again at the same time.
What is the LCM of 2,4, and 7
The LCM of 2,4,7 is 28. So, 28 is the smallest multiple shared by the numbers 2, 4, and 7. We can get the exact value of LCM of 2,4,7 through various methods. Let us see how
How to find the LCM of 2,4, and 7
To find the LCM of 2,4,7 we apply some methods. Those methods are:
- Listing Method
- Prime Factorization Method
- Division Method
LCM of 2,4, and 7 Using Listing the Multiples
The LCM of 2,4, and 7 can be found using the following steps:
Step 1: Write down the multiples of each number
Multiples of 2 = 2,4,6,8,10,12,14,16,18,20,24,26,28,30,....,200
Multiples of 4= 4,8,12,16,20,24,28,32,36,40,....,400
Multiples of 7 = 7,14,21,28,35,42,49,56,63,70,......,700
Step 2: Find out the smallest multiple from the listed multiples
The smallest common multiple is 28
Thus, LCM (2,4,7) = 28.
LCM of 2,4, and 7 Using Prime Factorization
The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.
Step 1: Find the prime factors of the numbers:
Prime factorization of 2 = 2×1
Prime factorization of 4 = 2×2
Prime factorization of 7 = 7×1
Step 2: Take the highest powers of each prime factor, and multiply the highest powers to get the LCM:
2×2×7 = 28
LCM (2,4,7) = 28.
LCM of 2,4, and 7 Using Division Method
This method involves dividing both numbers by their common prime factors until no further division is possible, then multiplying the divisors to find the LCM.
Step 1: Write the numbers, divide by common prime factors and multiply the divisors.
Step 2: A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of 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.
2×2×7 = 28
Thus, LCM (2,4,7) = 28
Common Mistakes and How to Avoid Them in LCM of 2,4, and 7
LCM of 2,4, and 7 Examples
Problem 1
The LCM of two numbers is 224 and the numbers are in the ratio 4:7. Find the numbers.
Explanation
Problem 2
LCM (2,4,7) = x. Find the smallest positive integer (n), where n×x=14.
Explanation
Problem 3
What is the LCM of 20, 2, and 4?
Explanation
FAQs on LCM of 2,4 and 7
1.List the multiples of 2,4 and 7.
2.What is the LCM of 2,6 and 30?
3.What is the LCM of 2,4,6,10 and 20?
4.What is the LCM of 15,25 and 45?
5.What is the LCM of 20,25 and 30?
Important glossaries for the LCM of 2,4 and 7
- 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.
