175 LearnersLast updated on May 26th, 2025
LCM of 14 and 22
The smallest positive integer that divides the numbers with no numbers left behind is the LCM of 14 and 22. Did you know? We apply LCM unknowingly in everyday situations like setting alarms and to synchronize traffic lights and when making music. In this article, let’s now learn to find LCMs of 14 and 22.
What is LCM of 14 and 22
We can find the LCM using listing multiples method, prime factorization method and the long division method. These methods are explained here, apply a method that fits your understanding well.
LCM of 14 and 22 using listing multiples method
Step 1: List the multiples of each of the numbers;
14 = 14,28,42,56,70,84,98,112,126,140,154…
22 = 22,44,66,88,110,132,154,…
Step 2: Find the smallest number in both the lists
LCM (14,22) = 154
LCM of 14 and 22 using prime factorization method
Step 1: Prime factorize the numbers
14 = 2×7
22= 11×2
Step 2:find highest powers
Step 3:Multiply the highest powers of the numbers
LCM(14,22) = 154
LCM of 14 and 22 using division method
- Write the numbers in a row
- Divide them with a common prime factor
- Carry forward numbers that are left undivided
- Continue dividing until the remainder is ‘1’
- Multiply the divisors to find the LCM
- LCM (14,22) = 154
Common mistakes and how to avoid them in LCM of 14 and 22
Listed here are a few mistakes children may make when trying to find the LCM due to confusion or due to unclear understanding. Be mindful, understand, learn and avoid!
Mistake 1
Duplicating or skipping a factor
A factor may be missed when we prime factorize a number. Writing the prime factorization of 22 may be written as 4×11 instead of 2×11 accidentally.
LCM of 14 and 22 Examples
Problem 1
Two numbers have an LCM of 154. One of the numbers is 14. Find the missing number.
Let the missing number be x
We know:
LCM(14,x)=154
Since the LCM of 14 and 22 is 154, x=22
Explanation
The LCM remains the same when the two numbers involved are 14 and 22, which confirms that the missing number is 22.
Problem 2
Let A={x∈Z:x is a multiple of 14} and B={x∈Z:x is a multiple of 22}B. Find the least positive integer in A∩B.
The least positive integer in A∩B is the LCM of 14 and 22, which is 154.
Explanation
The intersection of sets A and B contains all numbers that are multiples of both 14 and 22. The smallest such number is their LCM.
Problem 3
Find the LCM of the fractions 14/22​ and 22/14​.
The LCM of two fractions is given by the formula:
LCM(a/b, c/d)=LCM(a, c)/GCD(b, d)
Here:
a=14, b=22, c=22, d=14
LCM(14,22)=154,GCD(22,14)=2
Therefore:
LCM(14/22,22/14)=154/2=77
Explanation
The LCM of fractions uses both the LCM of the numerators and the GCD of the denominators to compute the result.
FAQs on the LCM of 14 and 22
1.What is the GCF of 14 and 22?
2.Find the LCM of 14 and 122.
3.What is the LCM of 14 and 21?
4.What is the LCM of 14 and 24?
5. What is the LCM of 13 and 22?
6.How can children in India use numbers in everyday life to understand LCM of 14 and 22 ?
7.What are some fun ways kids in India can practice LCM of 14 and 22 with numbers?
8.What role do numbers and LCM of 14 and 22 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve LCM of 14 and 22 skills?
Important glossaries for LCM of 14 and 22
- Multiple: the result after multiplication of a number and an integer. To explain, 75×5 =375; 375 is a multiple of 75.
- Prime Factor: A number with only two factors, 1 and the number. For example,7, its factors are only 1 and 7 and the number when divided by any other integer will leave a remainder behind.
- Prime Factorization: breaking a number down into its prime factors. For example, 60 is written as the product of 2×2×3×5.
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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
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