Last updated on May 26th, 2025
LCM of any two numbers is the least common multiple of two numbers. In our daily life, LCM is used for scheduling events, and distributing any items among others. In this topic, we will learn more about LCM of 10 and 18.
The common multiples\ of 10 and 18 is 90. Here, we will learn about the LCM of 2 numbers. Children learn about LCM at younger ages. Here, we will discuss the methods used for finding out LCM.
Out of many methods, prime factorization method is widely used for its easy approach. Here, we will learn about other methods as well. A few commonly used methods are as follows -
Listing multiples can be a tedious method for finding the LCM. Here, the listing of multiples for all these 2 numbers is noted -
Then we can see that out of 10 and 18, 90 is the smallest common number that is present in them. So we see that 90 is the LCM of 10 and 18.
The product of the highest power of prime factors of 10 and 18 is the LCM of these numbers. So let us look at it step by step to understand it better.
Breaking the given numbers into their prime factors.
Prime factorization of 10: 2 × 5
Prime factorization of 18: 2 × 32
Multiplying the highest power of prime factors: 2 × 32 × 51 → 2 × 9 × 5 = 90
LCM of 10 and 18 is 90.
In this method, we will be dividing the given numbers with the common prime factors until all numbers are reduced to 1. Let us look at this step by step and make it easy for the children to learn it.
Step 1: Arrange the number in a sequence, divisors, and the numbers are on the left and right sides respectively.
Step 2: For finding the divisor, it is always the smallest common prime factor. Here, the smallest common prime factor is 2. Dividing 10 and 18 by 2. The result is 5 and 9.
Step 3: As 9 is divisible by 3, the divisor is 3. Dividing 5 and 9 by 3. Now the result is 5 and 3.
Step 4: Continue dividing the numbers with the smallest prime number until all numbers are reduced to 1.
The divisors are 2, 3, 3, 5. LCM of 10 and 18 is the product of divisors.
Hence, the LCM of (10 and 18) = 2 × 3 × 3 × 5 = 90
There are some common mistakes that are made by children while solving a problem on LCM. Let us look at some of these mistakes and how we can help children to avoid these mistakes.
The product of the two numbers is 180 and their GCF is 2, what is their LCM?
Given :
The product of two numbers is 180
GCF = 2
So the LCM of two numbers,
LCM = product of the number / GCF
LCM = 180/2 =90
So the LCM of two numbers is 90.
Here, also given the product of the two numbers and GCF. When we find the LCM, we divide the product of the numbers by GCD. Then we get the LCM of 90.
Two alarms ring at intervals of 10 and 18 minutes, respectively. If both alarms ring together at 8:00 AM, when will they ring together?
by prime factorization :
10 = 2 × 5
18 = 2 × 32
LCM = 2 × 3 × 3 × 5 =90
When we find they will be together again, first we calculate the LCM of 10 and 18. We get the LCM of 10 and 18 is 90. So they will be together again in 90 minutes, or at 9: 30 AM.
A school schedules science class every 10 days and math class every 18 days. If both classes are held on the same day today, when will both classes happen on the same day again?
We find the LCM of 10 and 18 to determine when both events will align.
The LCM of 10 and 18 is 90
Both classes will be held on the same day again in 90 days.
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.