Last updated on May 26th, 2025
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 2 and 7. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. In our daily life, we use application of LCM for setting alarms in our clock or coordinating any orders.
The LCM of 2 and 7 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations 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;
The LCM of 2 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,…
Multiples of 7 = 7,12,21,14…
Step 2: Ascertain the smallest multiple from the listed multiples of 2 and 7.
The LCM (The Least common multiple) 2 and 7 is 14, i.e.,14 is divisible by 2 and 7 leaving no reminders.
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
Prime factorization of 7 = 7
Step 2:Take the highest power of each prime factor:
2,7
Step 3: Multiply the ascertained factors to get the LCM:
LCM (2,12) = 2×7 = 14
The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM.
Step 1: Write down the numbers in a row;
Step 2: Divide the row of numbers by a prime number that is evenly divisible into at least one of the given numbers. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers has not been divisible previously.
Step 2: The LCM of the numbers is the product of the prime numbers in the first column, i.e,
2×7= 14
LCM (2,7) = 14
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 2 and 7, make a note while practicing.
What is the least common denominator of 3/2 and 5/7 ?
LCM of 2 and 7 = 14
LCM of a and b is 14. If a is 2, can b be a divisor of 14?
LCM of a and b is 14. If a is 2, can b be a divisor of 14?
Yes.
b can be a divisor of 14. The LCM is the smallest multiple between the numbers, if a is 2, and the LCM is 14, the other number b must contribute necessary factors to form 14. The divisors of 14 include 7 and 14 itself.
From the above, we can assume that the other number b can be 14 or 7.
If 7, is b; → LCM(2,7) = 14, since 2 and 7 have no common factors, the LCM is simply their product.
If 14, is b → LCM(2,14) = 14, since 14 is a multiple of both 2 and 7.
Alex and Ben want to share a pizza, but they can’t decide how many slices to cut into. Alex says 2, and Ben says 7. What is the minimum number of slices they can cut the pizza into so that both can have their desired number of slices without leftovers?
The LCM of 2 and 7 is 14.
Alex and Ben should cut the pizza into 14 slices, which is the LCM of 2 and 7.
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.