# What is LCM of 60 and 84?

LCM of 60 and 84 is 420

#### How to find lcm of two numbers

 1.   What is LCM? 2.   Steps to find LCM of 60 and 84 By Listing Method 3.   Steps to find LCM of 60 and 84 By Common Division Method 4.   Steps to find LCM of 60 and 84 By Formula 5.   Examples

#### Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 60 and 84, is defined as the smallest positive integer that is divisible by both. It is written as LCM(60, 84).

#### Properties of LCM

• The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 60 and 84 is 420, where 60 and 84 are less than 420.
• LCM is associative which means LCM(60, 84) = LCM(84, 60).
• LCM is commutative which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
• LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).
• The LCM of two or more prime numbers is their product.

### Example: Find lcm of 60 and 84 by Listing Method

• Multiples of 60: 60, 120, 180, 240, 300, 360, 420, 480, 540, 600, 660, 720, 780, 840, 900, 960, 1020, 1080, 1140, 1200, 1260, 1320, 1380, 1440, 1500, 1560, 1620, 1680, 1740, 1800, 1860, 1920, 1980, 2040, 2100, 2160, 2220, 2280, 2340, 2400, 2460, 2520, 2580, 2640, 2700, 2760, 2820, 2880, 2940, 3000, 3060, 3120, 3180, 3240, 3300, 3360, 3420, 3480, 3540, 3600, 3660, 3720, 3780, 3840, 3900, 3960, 4020, 4080, 4140, 4200, 4260, 4320, 4380, 4440, 4500, 4560, 4620, 4680, 4740, 4800, 4860, 4920, 4980, 5040
• Multiples of 84: 84, 168, 252, 336, 420, 504, 588, 672, 756, 840, 924, 1008, 1092, 1176, 1260, 1344, 1428, 1512, 1596, 1680, 1764, 1848, 1932, 2016, 2100, 2184, 2268, 2352, 2436, 2520, 2604, 2688, 2772, 2856, 2940, 3024, 3108, 3192, 3276, 3360, 3444, 3528, 3612, 3696, 3780, 3864, 3948, 4032, 4116, 4200, 4284, 4368, 4452, 4536, 4620, 4704, 4788, 4872, 4956, 5040

Hence, LCM of 60 and 84 is 420.

### Example: Find lcm of 60 and 84 by Common Division Method

 2 60 84 2 30 42 3 15 21 5 5 7 7 1 7 1 1

Hence, LCM of 60 and 84 is 2 x 2 x 3 x 5 x 7 = 420.

### Example: Find lcm of 60 and 84 by Formula

• GCF of 60 and 84 = 12
• LCM of 60 and 84 = (60 x 84) / 12
• => 5040 / 12

Hence, LCM of 60 and 84 is 420.

#### Examples

Ram and Deepika are running on a circular track. They start at the same time. They take 60 and 84 minutes respectively to go round once. Find at what time they will run together?

Ram and Deepika are running on a circular track. They take 60 and 84 minutes respectively to go round once. We need to find out at what time (minimum) they will run together again. For this we need to find the LCM of 60 and 84.
So, LCM of 60 and 84 is 420.

A shopkeeper sells candies in packet of 60 and chocolates in packet of 84. What is the least number of candies and chocolates Annie should buy so that there will be one candy for each chocolate?

The least number of candies and chocolates Annie should buy so that there will be one candy for each chocolate we need to find the lcm of 60 and 84.
So, LCM of 60 and 84 is 420.

What is the relation between LCM and GCF( Greatest Common Factor)?

Greatest common factors or gcf of 60 and 84 is GCF(60, 84) * LCM(60, 84) = (60 x 84) / GCF(60, 84) = 420.

Sammy's company prints 60 textbooks at a time. Daniel's company prints textbooks in sets of 84 at a time. According to a survey done by a committee, both companies printed the same number of textbooks last year. Find the least number of books that each company would have printed.

To find the least number of textbooks that each company could have printed we need to find the LCM of 60 and 84.
So, LCM of 60 and 84 is 420.

Mary exercises every 60 days and Nikki every 84 days. They both excercised today. How many days will it be until they excercise together again?

The problem can be solved using LCM, because we are trying to figure out the least time until they excercise together again.
So, LCM of 60 and 84 is 420.

Find the least common multiple of 60 and 84.

Least common multiple of 60 and 84 is 420.

Find the least number which is exactly divisible by 60 and 84.

Least number which is exactly divisible by 60 and 84 is 420.