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135 LearnersLast updated on November 27th, 2024
LCM Of 42 And 72
The Least Common Multiple (LCM) is the smallest number that when we divide by two or more numbers at a time, all three or more numbers divide into it. LCM also helps in math problems and everyday things like event planning or buying supplies. We will find the LCM of 42 and 72 together and what that really means.
What Is The LCM Of 42 And 72?
The LCM or the least common multiple of 2 numbers is the smallest number that appears as a multiple of both numbers. In case of 42 and 72, The LCM is 504. But how did we get to this answer? There are different ways to obtain a LCM of 2 or more numbers. Let us take a look at those methods.
How To Find The LCM Of 42 And 72
Remember that we previously said there are plenty of ways to calculate the LCM of two numbers or more. Then some of those methods make it extremely easy for us to find the LCM of any two numbers. Those methods are:
- Listing of Multiples
- Prime Factorization
- Division Method
Finally, now we will learn how each of these methods can help us to calculate LCM of given numbers.
Finding LCM Of 42 And 72 By Listing Of Multiples
This method will help us find the LCM of the numbers by listing the multiples of the given numbers. Let us take a step by step look at this method.
The first step is to list all the multiples of the given numbers.
Multiples Of 42: 42, 84, 126, 168, 210, 252, 294, 336, 378, 420, 462, 504, 546, 588, 630, 672, 714, 756, 798, 840
Multiples Of 72: 72, 144, 216, 288, 360, 432, 504, 576, 648 and 720.
The second step is to find the smallest common multiples in both the numbers. In this case, that number is 504 as highlighted above.
By this way we will be able to tell the LCM of given numbers.
Finding The LCM By Prime Factorization
Let us break down the process of prime factorization into steps and make it easy for children to understand.
The first step is to break down the given numbers into its primal form. The primal form of the number is:
42= 2×3×7
72= 2×2×2×3×3
As you can see, 2 and 3 appears as a prime factor in both numbers. So instead of considering 2 four times, we will only consider it thrice and instead of considering 3 three time, we will consider it only twice. So the final equation will look like (2×2×2×3×3×7).
So after the multiplication, we will be getting the LCM as 504.
As you can see, using this method can be easier for larger numbers compared to the previous method.
Finding The LCM By Division Method
The method to calculate the LCM is really simple. We’ll break these given numbers apart till it comes down to one, by dividing it by the prime factors. The product of the divisors that will come is the LCM of the given numbers.
Let us understand it step by step:
- The first thing is to find the number common in both the numbers. Here it is 3. In that case, we divide both the numbers by 3. It will reduce the values of the numbers to 14 and 24.
- Then we will divide 24 and 14 by 2. This will give us 7 and 12. As 7 is a prime number, it can only be divided by 7. So, that is brought to its base form. Now, we divide 12 by 2 and bring it down to 6. The 6 can be divided by 3 again, and it will become 2. As 2 is a prime number, it can only be divided by 2 and is brought to its base form.
- As the numbers in the last row now are 1, we will take the numbers on the left side and find the product of those numbers. The final equation will look like this: (3×2×7×2×3×2).
These numbers multiplied give 504. On this basis, therefore, the LCM of the 42 and 72 becomes 504.
Common Mistakes That Are Made And How To Avoid Them in LCM Of 42 And 72.
LCM Of 42 And 72 Examples
Problem 1
If a party has 42 balloons and 72 streamers, what is the least number of decorations that can be equally arranged?
Explanation
Problem 2
A school has 42 red books and 72 blue books. What is the least number of book stacks for equal distribution?
Explanation
Problem 3
If a bus comes every 42 minutes and another every 72 minutes, when will they come together again?
Explanation
Problem 4
Two racers finish their laps in 42 seconds and 72 seconds. When will they finish together again?
Explanation
Problem 5
In a game, if players score every 42 and 72 points, when do they reach the same score?
Explanation
FAQs On LCM Of 42 And 72
1.What is the LCM of 42 and 72?
2.Is 504 divisible by both 42 and 72?
3.Is the LCM of 42 and 72 even or odd?
4.Is the LCM of 42 and 72 bigger than either number?
Important Glossaries for LCM of 42 and 72
- Least Common Multiple (LCM): The smallest number that can be divided evenly by two or more numbers. It helps us find common ground when working with different groups.
- Prime Number: A number greater than 1 that can only be divided by 1 and itself. For example, 2, 3, 5, and 7 are prime numbers.
- Remainder: What is left over after division when one number does not divide another evenly. For example, in 10 ÷ 3, the remainder is 1.
- Prime Factorization: Breaking down a number into its basic building blocks (prime numbers). For example, 42 can be broken down into 2 × 3 × 7.
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