Hi, My kitchen sink is next to the wasing machine. Every time when my washer drains the water out I get water backing up out of my kitchen sink. To me it seems like the 1 1/2 inch drain pipe in my laundry room cannot handle the large load of water that is draining out of the washer.

You are correct: your washing machine should have 2" drain to absorb all outgoing water w/o backing up.

However, as it was discussed here many times before, the core of the problem is that your washer shares same drain with kitchen sink. Kitchen drain is usually the most blocked drain in whole house. It is unable to drain all the water discharge by your washer so it backs up to the sink.

You have to snake kitchen drain. You could have clean-out plug either under the sink inside your cabinet or on the wall behind the sink. Rent a 3/8" snake from Home Depot and snake it entire length of snake several times. Flush with lots of water.

Hi, My kitchen sink is next to the wasing machine. Everytime when my washer drains the water out i get water backing up out of my kitchen sink. To me it seems like the 1 1/2 inch drain pipe in my laundry room cannot handle the large load of water that is draining out of the washer.
Hey Pokey,
This is the double whammy we've been warning builders about for years. Mix fiber and grease from the washer with garbage and more grease from the kitchen sink and drain the mess through a 1 1/2" line and you're going to have back ups and complaints.
For this clog you're not going to clear it by snaking the laterial drain line from under the kitchen cabinet. The clog's downstream from the washer. You will have to come down the kitchen roof vent to clear this one. Put out enough cable to reach the base and 20 feet more. Flu out after with a garden hose down the vent. Good luck, Tom