# Online Pre-Algebra Tutoring: Common Multiples

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A common multiple is a number that is a multiple of two or more numbers.

Least common multiple is the smallest multiple shared between two or more numbers. The Least Common Multiple **(LCM)** is also referred to as the Least Common Denominator **(LCD)**.

**Steps to find the LCM:**

â€¢Factor both numbers to their primes

â€¢Identify any shared primes

â€¢Take the shared prime and multiply it with all of the other prime factors

## Learn Â about common Multiples Â from Certified Online Pre-Algebra Tutor

**What is the LCM of 24 and 32?**

First, we factor both numbers to their primes.

The prime factorization of 24 is:

**24 = 2 x 2 x 2 x 3 **

The prime factorization of 32 is:

**32 = 2 x 2 x2 x 2 x 2 **

Next, we identify any shared primes. With 24 and 32, 2 x 2 x 2 is a shared prime number.

Then, we take the shared prime and multiply it with all of the other prime factors.

**2 x 2 x2Â 3Â 2Â 2**

The red 2 x 2 x2 is the shared prime factor.

The blue numbers are the other prime factors.

#### Our answer is 96. The LCM of 32 and 24 is 96.

### Check Point

**a)** Find the L.C.M. of 12, 27

**b)** Find the L.C.M. of 125,64,8

**c)** Quincy is buying flower bulbs for his garden. He wants to buy the same number of tulips and daffodils. If tulip bulbs come in packs of 28 and daffodil bulbs come in packs of42, what is the least number of each type of bulb Quincy will need to buy?

**d)** In a morning walk, three persons step off together. Their steps measure 85 cm, 70 cm and 90 cm respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps?

**e)** The traffic lights at three different road crossings change after every 12 seconds, 18 seconds and 22 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again?

**Answer key**

**a)** 108.

**b)** 8000

**c)** 84 flower bulbs

**d)** 10,710 cm

**e)** All the traffic lights will change simultaneously change after 396 seconds which is equal to 6 min 36 seconds past 7 am.

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