# What is LCM of 75 and 120?

LCM of 75 and 120 is 600

#### How to find lcm of two numbers

 1.   What is LCM? 2.   Steps to find LCM of 75 and 120 By Listing Method 3.   Steps to find LCM of 75 and 120 By Common Division Method 4.   Steps to find LCM of 75 and 120 By Formula 5.   Examples

#### Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 75 and 120, is defined as the smallest positive integer that is divisible by both. It is written as LCM(75, 120).

#### Properties of LCM

• The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 75 and 120 is 600, where 75 and 120 are less than 600.
• LCM is commutative which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
• The LCM of two or more prime numbers is exactly equal to their product.
• LCM is associative which means LCM(75, 120) = LCM(120, 75).
• LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).

### Example: Find lcm of 75 and 120 by Listing Method

• Multiples of 75: 75, 150, 225, 300, 375, 450, 525, 600, 675, 750, 825, 900, 975, 1050, 1125, 1200, 1275, 1350, 1425, 1500, 1575, 1650, 1725, 1800, 1875, 1950, 2025, 2100, 2175, 2250, 2325, 2400, 2475, 2550, 2625, 2700, 2775, 2850, 2925, 3000, 3075, 3150, 3225, 3300, 3375, 3450, 3525, 3600, 3675, 3750, 3825, 3900, 3975, 4050, 4125, 4200, 4275, 4350, 4425, 4500, 4575, 4650, 4725, 4800, 4875, 4950, 5025, 5100, 5175, 5250, 5325, 5400, 5475, 5550, 5625, 5700, 5775, 5850, 5925, 6000, 6075, 6150, 6225, 6300, 6375, 6450, 6525, 6600, 6675, 6750, 6825, 6900, 6975, 7050, 7125, 7200, 7275, 7350, 7425, 7500, 7575, 7650, 7725, 7800, 7875, 7950, 8025, 8100, 8175, 8250, 8325, 8400, 8475, 8550, 8625, 8700, 8775, 8850, 8925, 9000
• Multiples of 120: 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200, 1320, 1440, 1560, 1680, 1800, 1920, 2040, 2160, 2280, 2400, 2520, 2640, 2760, 2880, 3000, 3120, 3240, 3360, 3480, 3600, 3720, 3840, 3960, 4080, 4200, 4320, 4440, 4560, 4680, 4800, 4920, 5040, 5160, 5280, 5400, 5520, 5640, 5760, 5880, 6000, 6120, 6240, 6360, 6480, 6600, 6720, 6840, 6960, 7080, 7200, 7320, 7440, 7560, 7680, 7800, 7920, 8040, 8160, 8280, 8400, 8520, 8640, 8760, 8880, 9000

Hence, LCM of 75 and 120 is 600.

### Example: Find lcm of 75 and 120 by Common Division Method

 2 75 120 2 75 60 2 75 30 3 75 15 5 25 5 5 5 1 1 1

Hence, LCM of 75 and 120 is 2 x 2 x 2 x 3 x 5 x 5 = 600.

### Example: Find lcm of 75 and 120 by Formula

• GCF of 75 and 120 = 15
• LCM of 75 and 120 = (75 x 120) / 15
• => 9000 / 15

Hence, LCM of 75 and 120 is 600.

#### Examples

Franky and Joy are running on a circular track. They start at the same time. They take 75 and 120 minutes respectively to go round once. Find at what time they will run together?

Franky and Joy are running on a circular track. They take 75 and 120 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 75 and 120.
So, LCM of 75 and 120 is 600.

Both the cricket team and the rugby team had games, today. The cricket team plays every 75 days and the basketball team plays every 120 days. When will both teams have games on the same day again?

Given that the cricket team plays every 75 days and the basketball team plays every 120 days, so for finding the next time when both teams will play again we need to find the LCM of 75 and 120.
So, LCM of 75 and 120 is 600.

Steve spends 75 dollars every day while George spends 120 dollars every day. What is the least number of days it will take each person to spend the same amount of money?

To find the least number of days that would be taken to be able to spend the same amount of dollars we need to find the LCM of 75 and 120.
So, LCM of 75 and 120 is 600.

Boxes that are 75 inches tall are being pilled next to boxes that are 120 inches tall. What is the least height in feet at which the two piles will be the same height?

To find the least height in feet at which the two piles will be at same height we will find LCM of 75 and 120.
So, LCM of 75 and 120 is 600.

Find the LCM of 75 and 120 using GCF method.

Greatest common factor or gcf of 75 and 120 is GCF(75, 120) x LCM(75, 120) = (75 x 120) / GCF(75, 120) = 600.

Find the least common multiple of 75 and 120.

Least common multiple of 75 and 120 is 600.

Find the least number which is exactly divisible by 75 and 120.

Least number which is exactly divisible by 75 and 120 is 600.