150 LearnersLast updated on May 26th, 2025
LCM of 63 and 21
Least Common Multiple (LCM) is the smallest positive integer that is divisible by both 63 and 21. By learning the following tricks, you can learn the LCM of 63 and 21 easily.
What Is the LCM of 63 and 21?
The LCM of 63 and 21 is 63. How did we get to this answer, though? That’s what we’re going to learn. We also see how we can find the LCM of 2 or more numbers in different ways.
How to find the LCM of 63 and 21?
We have already read about how you can approach finding the LCM of 2 or more numbers. Here is a list of those methods which make it easy to find the LCMs:
Method 1: Listing of Multiples
Method 2: Prime Factorization
Method 3: Division Method
Now let us delve further into these three methods and how it benefits us.
LCM of 63 and 21 Using Listing of Multiples Method
In this method, we will list all the multiples of 63 and 21. Then we will try to find a multiple that is present in both numbers.
For example,
Multiples of 63:
63, 126, 189, 252, 315, 378, 441, 504, 567, 630,....
Multiples of 21:
21, 42, 63, 84, 105, 126, 147, 168, 189, 210,…
The LCM of 63 and 21 is 63. 63 is the smallest number which can be divisible by both 63 and 21.
LCM of 63 and 21 Using Prime Factorization
To find the LCM of 63 and 21 using the prime factorization method, we need to find out the prime factors of both the numbers. Then multiply the highest powers of the factors to get the LCM.
Prime Factors of 63 are: 32, 71.
Prime Factors of 21 are: 31, 71.
Multiply the highest power of both the factors: 33 × 71 = 3 × 3 × 7 = 63
Therefore, the LCM of 63 and 21 is 63
LCM of 63 and 21 Using Division Method
To calculate the LCM using the division method. We will divide the given numbers with their prime numbers. The prime numbers should at least divide any one of the given numbers. Divide the numbers till the remainder becomes 1. By multiplying the prime factors, one can get LCM.
For finding the LCM of 63 and 21 we will use the following method.
By multiplying the prime divisors from the table, we will get the LCM of 63 and 21.
3 × 3 × 7 = 63
The LCM of 63 and 21 is 63.
Common Mistakes and How To Avoid Them in LCM of 63 and 21.
Mistakes are common when we are finding the LCM of numbers. By learning the following common mistakes, we can avoid the mistakes.
Mistake 1
Missing a prime factor
Children sometimes may forget to write all the prime factors for a given number. So, at the start we have to write all the prime factors for the given numbers which won’t cause any problems later on.
LCM of 63 and 21 Examples
Problem 1
Machine A and B complete a cycle every 21 minutes, and 63 minutes respectively. If they both start at the same time in how many minutes will they complete a cycle together again, and what percentage of an hour will that be?
Find the LCM of 21 and 63, which is 63. This means both machines will complete a cycle together every 63 minutes.
Convert 63 minutes to a percentage of an hour: 63/60 × 100 = 105%
Explanation
The LCM tells us when both cycles will sync up again. By dividing the 63 minutes by 60 (the minutes in an hour), we convert this to a percentage. As 63 minutes are more than an hour, equal 105% of an hour.
Problem 2
Alex and Bob work on a task, where Alex completes a cycle every 21 minutes, and Bob completes one every 63 minutes. If they both start together, how long before both are available to work on the task together again?
Since we already calculated the LCM of 21 and 63, which is 63 minutes, they will both be ready to start another cycle together after 63 minutes.
Explanation
The LCM gives the shortest interval where both work cycles overlap, showing when both Alex and Bob will be ready simultaneously.
Problem 3
Verify the relationship between the LCM and GCF of 21 and 63 by using the formula: LCM (a, b) × GCF (a, b) = a×b for a=21 and b=63.
LCM(21, 63) = 63 (from previous calculation)
Calculate the GCF of 21 and 63:
The common factors are 3 and 7, so GCF(21, 63) = 21.
Verify: LCM (21,63) × GCF(21,63) = 63 × 21 = 1323
The product of the LCM and GCF of any positive numbers is equal to the product of the numbers.
Explanation
The LCM and GCF of two numbers equals the product of the numbers themselves.
FAQs on the LCM of 63 and 21
1.What is the GCF of 21 and 63?
2. Is 63 a multiple of 21?
3. Is 21 a factor of 63?
4.What goes into 21 and 63?
5.What is LCD? What is the LCD of 21 and 63?
6.How can children in Qatar use numbers in everyday life to understand LCM of 63 and 21?
7.What are some fun ways kids in Qatar can practice LCM of 63 and 21 with numbers?
8.What role do numbers and LCM of 63 and 21 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve LCM of 63 and 21 skills?
Important Glossaries for the LCM of 63 and 21
- Prime Number: Any number that has only 2 factors is called a prime number.For example, 5 and 7, only common factors are 1 and the number itself.
- Composite Number: Any number that has more than 2 factors is called a composite number. For example, 4, 8, and 10.
- Prime Factorization: It is breaking down a number into smaller prime numbers, then multiplied together, giving the same number.
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About BrightChamps in Qatar
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.
