# What is LCM of 105 and 175?

LCM of 105 and 175 is 525

#### How to find lcm of two numbers

 1.   What is LCM? 2.   Steps to find LCM of 105 and 175 By Listing Method 3.   Steps to find LCM of 105 and 175 By Common Division Method 4.   Steps to find LCM of 105 and 175 By Formula 5.   Examples

#### Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 105 and 175, is defined as the smallest positive integer that is divisible by both. It is written as LCM(105, 175).

#### Properties of LCM

• The LCM of two or more prime numbers is exactly equal to their product.
• LCM is associative which means LCM(105, 175) = LCM(175, 105).
• 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 given numbers is always greater than the given numbers numbers. Eg- LCM of 105 and 175 is 525, where 525 is greater than 105 and 175.

### Example: Find lcm of 105 and 175 by Listing Method

• Multiples of 105: 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050, 1155, 1260, 1365, 1470, 1575, 1680, 1785, 1890, 1995, 2100, 2205, 2310, 2415, 2520, 2625, 2730, 2835, 2940, 3045, 3150, 3255, 3360, 3465, 3570, 3675, 3780, 3885, 3990, 4095, 4200, 4305, 4410, 4515, 4620, 4725, 4830, 4935, 5040, 5145, 5250, 5355, 5460, 5565, 5670, 5775, 5880, 5985, 6090, 6195, 6300, 6405, 6510, 6615, 6720, 6825, 6930, 7035, 7140, 7245, 7350, 7455, 7560, 7665, 7770, 7875, 7980, 8085, 8190, 8295, 8400, 8505, 8610, 8715, 8820, 8925, 9030, 9135, 9240, 9345, 9450, 9555, 9660, 9765, 9870, 9975, 10080, 10185, 10290, 10395, 10500, 10605, 10710, 10815, 10920, 11025, 11130, 11235, 11340, 11445, 11550, 11655, 11760, 11865, 11970, 12075, 12180, 12285, 12390, 12495, 12600, 12705, 12810, 12915, 13020, 13125, 13230, 13335, 13440, 13545, 13650, 13755, 13860, 13965, 14070, 14175, 14280, 14385, 14490, 14595, 14700, 14805, 14910, 15015, 15120, 15225, 15330, 15435, 15540, 15645, 15750, 15855, 15960, 16065, 16170, 16275, 16380, 16485, 16590, 16695, 16800, 16905, 17010, 17115, 17220, 17325, 17430, 17535, 17640, 17745, 17850, 17955, 18060, 18165, 18270, 18375
• Multiples of 175: 175, 350, 525, 700, 875, 1050, 1225, 1400, 1575, 1750, 1925, 2100, 2275, 2450, 2625, 2800, 2975, 3150, 3325, 3500, 3675, 3850, 4025, 4200, 4375, 4550, 4725, 4900, 5075, 5250, 5425, 5600, 5775, 5950, 6125, 6300, 6475, 6650, 6825, 7000, 7175, 7350, 7525, 7700, 7875, 8050, 8225, 8400, 8575, 8750, 8925, 9100, 9275, 9450, 9625, 9800, 9975, 10150, 10325, 10500, 10675, 10850, 11025, 11200, 11375, 11550, 11725, 11900, 12075, 12250, 12425, 12600, 12775, 12950, 13125, 13300, 13475, 13650, 13825, 14000, 14175, 14350, 14525, 14700, 14875, 15050, 15225, 15400, 15575, 15750, 15925, 16100, 16275, 16450, 16625, 16800, 16975, 17150, 17325, 17500, 17675, 17850, 18025, 18200, 18375

Hence, LCM of 105 and 175 is 525.

### Example: Find lcm of 105 and 175 by Common Division Method

 3 105 175 5 35 175 5 7 35 7 7 7 1 1

Hence, LCM of 105 and 175 is 3 x 5 x 5 x 7 = 525.

### Example: Find lcm of 105 and 175 by Formula

• GCF of 105 and 175 = 35
• LCM of 105 and 175 = (105 x 175) / 35
• => 18375 / 35

Hence, LCM of 105 and 175 is 525.

#### Examples

Franky and Joy are running on a circular track. They start at the same time. They take 105 and 175 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 105 and 175 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 105 and 175.
So, LCM of 105 and 175 is 525.

A shopkeeper sells candies in packet of 105 and chocolates in packet of 175. 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 105 and 175.
So, LCM of 105 and 175 is 525.

Boxes that are 105 inches tall are being pilled next to boxes that are 175 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 105 and 175.
So, LCM of 105 and 175 is 525.

Sammy's company prints 105 textbooks at a time. Daniel's company prints textbooks in sets of 175 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 105 and 175.
So, LCM of 105 and 175 is 525.

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

Greatest common factors or gcf of 105 and 175 is GCF(105, 175) * LCM(105, 175) = (105 x 175) / GCF(105, 175) = 525.

Find the least number which is exactly divisible by 105 and 175.

Least number which is exactly divisible by 105 and 175 is 525.

Find the LCM of 105 and 175 using GCF method.

Greatest common factor or gcf of 105 and 175 is GCF(105, 175) x LCM(105, 175) = (105 x 175) / GCF(105, 175) = 525.