Last updated on May 26th, 2025
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.
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
To find the LCM of 2,4,7 we apply some methods. Those methods are:
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.
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.
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
Misconception is normal, but we should avoid it whenever we are solving math problems. Let us see how we can avoid some common errors.
The LCM of two numbers is 224 and the numbers are in the ratio 4:7. Find the numbers.
Since, the numbers are in the ratio 4:7, so let the numbers 4x and 7x.
LCM of 4x and 7x → 28x.
Now, 28x=224
⇒ x= 224/28
⇒ x = 8
Answer: 32 and 56
Expanded the ratio and assumed the numbers to be 4x and 7x. We know that their ratio is equal to the given ratio 224. Hence, solved the equation for that.
LCM (2,4,7) = x. Find the smallest positive integer (n), where n×x=14.
LCM (2,4,7) = x
We know that the LCM of 2,4,7 from the previous calculations.
LCM (2,4,7) = 28
n×28=14
⇒ n= 14/28
⇒ n =1/2
Answer: 1/2
We made use of the LCM OF 2,4,7 and solved the equation to get the value of n.
What is the LCM of 20, 2, and 4?
Multiple of 20: 20,40,60,....
Multiples of 2: 2,4,6,8,10,12,14,16,18,20,22,...
Multiples of 4: 4,8,12,16,20,24…..
So, LCM of 20,2,4 is 20
Answer: 20
The LCM of numbers 20,2,4 are found using the listing multiple method.
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.
: She loves to read number jokes and games.