Last updated on May 26th, 2025
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 7 and 14. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.
The LCM of 7 and 14 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations like addition and subtraction with fractions to equate the denominators.
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
To ascertain the LCM, list the multiples of the integers until a common multiple is found.
Step1:Writedown the multiples of each number:
Multiples of 7 = 7,14,…
Multiples of 14 = 14,28,…
Step2: Ascertain the smallest multiple from the listed multiples of 7 and 14.
The LCM (Least common multiple) of 7 and 14 is 14. i.e., 14 is divisible by 7 and 14 with no reminder.
This method involves finding the prime factors of each number and then multiplying the highest power of the prime factors to get the LCM.
Step1: Find the prime factors of the numbers:
Prime factorization of 7 = 7
Prime factorization of 14 = 2×7
Step2:Take the highest power of each prime factor: 7,2
Step3:Multiply the ascertained factors to get the LCM:
LCM (7,14) = 7×2 = 14
The Division Method involves dividing the numbers by their prime factors and multiplying the divisors to get the LCM.
Step1: Write down the numbers in a row;
Step2: Divide the row of numbers by a prime number that is evenly divisible into at least one of the given numbers.
Step3: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.
Step4: The LCM of the numbers is the product of the prime numbers in the first column, i.e.,
7×2= 14
LCM (7,14) = 14
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 7 and 14, make a note while practising.
The LCM of 7 and x is 14. Find x.
LCM (7,x) = 14
x = 14
The LCM of 7 and x must be 14. In a case where x is smaller, the LCM would not be 14,therefore x = 14.
Verify the relationship between the HCF and the LCM of 7 and 14 using LCM(a,b) × HCF(a,b) = a×b
The LCM of 7 and 14;
Prime factorization of 7 = 7
Prime factorization of 14 = 2×7
LCM(7,14) = 14
HCF of 7 and 14;
Factors of 7 = 1,7
Factors of 14 = 1,2,7,14
HCF(7,14) = 7
Verify the ascertained LCM and HCF by applying them in the formula;
LCM(a,b)×HCF(a,b) =a×b
LCM(7,14)×HCF(7,14) =7×14
14×7 =98
98 =98
Both sides are equal, hence, the relationship between the HCF and LCM of 7 and 14 is verified.
Solve 5/7 + 3/14.
To add 5/7 and 3/14, first, find the LCM of their denominators;
LCM (7,14) = 14
Now, we equate the denominators;
5/7 × 2/2 = 10/14
3/14 stays as it is, the denominator is already 14.
Add the fractions;
10/14+3/14 = 13/14
The sum is 13/14.
By equating the denominators of fractions, we can easily perform arithmetic operations on them.
Trains A and B arrive every 7 minutes and 14 minutes at the station at the same time. In how long will they arrive together again?
The LCM of 7 and 14 =14.
The smallest common multiple is ascertained between the numbers to ascertain the next arrival of the trains at the same time, which is in 14 minutes.
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.