Question

Find the LCM and hcf of 72 and 162 , leaving the LCM in prime factors
​

Answer 1

LCM= 648

HCF= 18

Step-by-step explanation:

Answer 2

Answers:

LCM = 2^3*3^4

HCF = 18

=========================================================

Step-by-step explanation:

Find the prime factorization of 72 and 162

• 72 = 8*9 = 2^3*3^2
• 162 = 2*81 = 2*9^2 = 2*(3^2)^2 = 2*3^4

Here's a simplified version of each

• 72 = 2^3*3^2
• 162 = 2*3^4

We have these unique primes: 2, 3

Circle the terms that have the largest exponents for each of those unique primes. So you'll circle 2^3 and 3^4. Those items circled will multiply together to get the LCM.

This means 2^3*3^4 is the LCM (lowest common multiple).

2^3*3^4 turns into 648, but your teacher wants you to keep the LCM in prime factor form.

------------------------------

Now onto the HCF (highest common factor; aka GCF).

Looking at

• 72 = 2^3*3^2
• 162 = 2*3^4

We again see '2's and '3's as the unique primes. Both have at 1 copy of '2' between them. They also both have 3^2 between them. It might help to think of 3^4 as 3^2*3^2.

Those common factors you circled are then multiplied.

Overall, the HCF is 2*3^2 = 2*9 = 18

-----------------------------

Side note: The HCF is useful to help reduce fractions, while the LCM is useful to help find the LCD (lowest common denominator) when adding or subtracting fractions of different denominators. There are other applications of each of these.