LCM of 72, 126 and 168 is 504. We can find the least common multiple of 72, 126 and 168 by using the methods such as prime factorisation, division method and list of multiples. Professional teachers suggest students make use of the article Least Common Multiple (LCM) while practising the problems based on the LCM. This also helps them to enhance their problem-solving and time management skills which are vital to score good marks in exams. Let us learn how to calculate the least common multiple of 72, 126 and 168 in a detailed manner here.
What is LCM of 72, 126 and 168?
The Least Common Multiple of 72, 126 and 168 is 504.
How to Find LCM of 72, 126 and 168?
LCM of 72, 126 and 168 can be determined using three methods
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 72, 126 and 168 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. The least common multiple will be the product of all prime factors with the highest degree.
72 = 2 × 2 × 2 × 3 × 3
126 = 2 × 3 × 3 × 7
168 = 2 × 2 × 2 × 3 × 7
LCM (72, 126, 168) = 2 × 2 × 2 × 3 × 3 × 7 = 504
LCM of 72, 126 and 168 Using Division Method
In the division method, to find the least common multiple of 72, 126 and 168, we divide the numbers 72, 126 and 168 by their prime factors until we get the result as one in the complete row. The product of these divisors gives the least common multiple of 72, 126 and 168.
| 2 | 72 | 126 | 168 |
| 2 | 36 | 63 | 84 |
| 2 | 18 | 63 | 42 |
| 3 | 9 | 63 | 21 |
| 3 | 3 | 21 | 7 |
| 7 | 1 | 7 | 7 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (72, 126, 168) = 2 × 2 × 2 × 3 × 3 × 7 = 504
LCM of 72, 126 and 168 Using Listing the Multiples
In this method, we list the multiples of 72, 126 and 168 to determine the least common multiple among them. Let us glance at the multiples of 72, 126 and 168 from the table given below.
| Multiples of 72 | Multiples of 126 | Multiples of 168 |
| 72 | 126 | 168 |
| 144 | 252 | 336 |
| 216 | 378 | 504 |
| 288 | 504 | 672 |
| 360 | 630 | 840 |
| 432 | 756 | 1008 |
| 504 | 882 | 1176 |
LCM (72, 126, 168) = 504
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Example
Question: What is the smallest number that is divisible by 72, 126, 168 exactly?
Solution: The smallest number that is divisible by 72, 126, 168 exactly is their LCM. We know that the LCM of 72, 126 and 168 is 504. Therefore the smallest number that is divisible by 72, 126, 168 exactly is 504.
Frequently Asked Questions on LCM of 72, 126 and 168
What is the LCM of 72, 126 and 168?
Is the LCM of 72, 126 and 168 the same as the HCF of 72, 126 and 168?
Name the methods used to find the least common multiple of 72, 126 and 168?
The methods used to find the least common multiple of 72, 126 and 168 are:
Prime Factorisation
Division method
Listing the Multiples
Calculate the LCM of 72, 126 and 168 with the help of the prime factorisation method.
In this method, to determine the LCM, we express the given numbers as the product of prime factors
72 = 2 × 2 × 2 × 3 × 3
126 = 2 × 3 × 3 × 7
168 = 2 × 2 × 2 × 3 × 7
LCM (72, 126, 168) = 2 × 2 × 2 × 3 × 3 × 7 = 504
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